Near Smoothly Undulating Primes

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Near Smoothly Undulating Primes (NSUP's) (with 6-digit undulators)
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“NSUP” Prime Projects

Hereunder at the left you'll find the table with files containing the primefactors of the SUPP's (Smoothly Undulating Palindromic Primes).
At the right you'll find the corresponding 6-digit NSUP's.

Case [k](d₁d₂d₃d₄d₅d₆)_u = [prefix](6-digit undulator).
Attentive readers of the factor lists will have noticed with me that some SUPP primefactors are themselves near smoothly undulating. 'Near' because of an initial prefix and the repeating 6-digit undulators.
We divide therefore the SUPP by primefactor 3 (see table 'Mark 3') or 7 (see table 'Mark 7').

SUPP (Smoothly Undulating Prime Palindromes) reference files

1(01)_w = (10*10ⁿ–1)/99 Factorization of Repunits (M. Kamada)

1(21)_w = (12*10ⁿ–21)/99 Factorization of 133...331 (M. Kamada)

1(31)_w = (13*10ⁿ–31)/99 Factorization of 144...441 (M. Kamada)

1(41)_w = (14*10ⁿ–41)/99 Factorization of 155...551 (M. Kamada)

1(51)_w = (15*10ⁿ–51)/99 Factorization of 166...661 (M. Kamada)

1(61)_w = (16*10ⁿ–61)/99 Factorization of 177...771 (M. Kamada)

1(71)_w = (17*10ⁿ–71)/99 Factorization of 188...881 (M. Kamada)

1(81)_w = (18*10ⁿ–81)/99 Factorization of 199...991 (M. Kamada)

1(91)_w = (19*10ⁿ–91)/99 facsupp191.htm (by P. De Geest).

3(13)_w = (31*10ⁿ–13)/99 Factorization of 344...443 (M. Kamada)

3(23)_w = (32*10ⁿ–23)/99 Factorization of 355...553 (M. Kamada)

3(43)_w = (34*10ⁿ–43)/99 Factorization of 377...773 (M. Kamada)

3(53)_w = (35*10ⁿ–53)/99 Factorization of 388...883 (M. Kamada)

3(73)_w = (37*10ⁿ–73)/99 facsupp373.htm (by P. De Geest).

3(83)_w = (38*10ⁿ–83)/99 facsupp383.htm (by P. De Geest).

7(17)_w = (71*10ⁿ–17)/99 Factorization of 788...887 (M. Kamada)

7(27)_w = (72*10ⁿ–27)/99 Factorization of 799...997 (M. Kamada)

7(37)_w = (73*10ⁿ–37)/99 facsupp737.htm (by P. De Geest).

7(47)_w = (74*10ⁿ–47)/99 facsupp747.htm (by P. De Geest).

7(57)_w = (75*10ⁿ–57)/99 facsupp757.htm (by P. De Geest).

7(87)_w = (78*10ⁿ–87)/99 facsupp787.htm (by P. De Geest).

7(97)_w = (79*10ⁿ–97)/99 facsupp797.htm (by P. De Geest).

9(19)_w = (91*10ⁿ–19)/99 facsupp919.htm (by P. De Geest).

9(29)_w = (92*10ⁿ–29)/99 facsupp929.htm (by P. De Geest).

9(49)_w = (94*10ⁿ–49)/99 facsupp949.htm (by P. De Geest).

9(59)_w = (95*10ⁿ–59)/99 facsupp959.htm (by P. De Geest).

9(79)_w = (97*10ⁿ–79)/99 facsupp979.htm (by P. De Geest).

9(89)_w = (98*10ⁿ–89)/99 facsupp989.htm (by P. De Geest).

[k](d₁d₂d₃d₄d₅d₆)_n = NSUP's (Near Smoothly Undulating Primes) Mark 3

1(01)_w Always Composite (Steps 3w are divisible by 37)

1(21)_w not divisible by 3 !

1(31)_w / 3 (13*10ⁿ–31)/(99*3) = [4377](104377)_u Step 6w + 5 Link

1(41)_w / 3 (14*10ⁿ–41)/(99*3) = [47](138047)_u Step 6w + 3 Link

1(51)_w not divisible by 3 !

1(61)_w / 3 (16*10ⁿ–61)/(99*3) = [5387](205387)_u Step 6w + 5 Link

1(71)_w / 3 (17*10ⁿ–71)/(99*3) = [57](239057)_u Step 6w + 3 Link

1(81)_w not divisible by 3 !

1(91)_w / 3 (19*10ⁿ–91)/(99*3) = [6397](306397)_u Step 6w + 5 Link

3(13)_w / 3 (31*10ⁿ–13)/(99*3) = [1](043771)_u Step 6w + 1 Link

3(23)_w / 3 (32*10ⁿ–23)/(99*3) = [1](077441)_u Step 6w + 1 Link

3(43)_w / 3 (34*10ⁿ–43)/(99*3) = [1](144781)_u Step 6w + 1 Link

3(53)_w / 3 (35*10ⁿ–53)/(99*3) = [1](178451)_u Step 6w + 1 Link

3(73)_w / 3 (37*10ⁿ–73)/(99*3) = [1](245791)_u Step 6w + 1 Link

3(83)_w / 3 (38*10ⁿ–83)/(99*3) = [1](279461)_u Step 6w + 1 Link

7(17)_w / 3 (71*10ⁿ–17)/(99*3) = [239](057239)_u Step 6w + 3 Link

7(27)_w / 3 not divisible by 3 !

7(37)_w / 3 (73*10ⁿ–37)/(99*3) = [24579](124579)_u Step 6w + 5 Link

7(47)_w / 3 (74*10ⁿ–47)/(99*3) = [249](158249)_u Step 6w + 3 Link

7(57)_w not divisible by 3 !

7(87)_w not divisible by 3 !

7(97)_w / 3 (79*10ⁿ–97)/(99*3) = [26599](326599)_u Step 6w + 5 Link

9(19)_w / 3 (91*10ⁿ–19)/(99*3) = [3](063973)_u Step 6w + 1 Link

9(29)_w / 3 (92*10ⁿ–29)/(99*3) = [3](097643)_u Step 6w + 1 Link

9(49)_w / 3 (94*10ⁿ–49)/(99*3) = [3](164983)_u Step 6w + 1 Link

9(59)_w / 3 (95*10ⁿ–59)/(99*3) = [3](198653)_u Step 6w + 1 Link

9(79)_w / 3 (97*10ⁿ–79)/(99*3) = [3](265993)_u Step 6w + 1 Link

9(89)_w / 3 (98*10ⁿ–89)/(99*3) = [3](299663)_u Step 6w + 1 Link

[k](d₁d₂d₃d₄d₅d₆)_n = NSUP's (Near Smoothly Undulating Primes) Mark 7

1(01)_w Always Composite (Steps 6w always divisible by 37)

1(21)_w not divisible by 7 !

1(31)_w not divisible by 7 !

1(41)_w not divisible by 7 !

1(51)_w not divisible by 7 !

1(61)_w / 7 (16*10ⁿ–61)/(99*7) = [23](088023)_u Step 6w + 3 Link

1(71)_w / 7 (17*10ⁿ–71)/(99*7) = [2453](102453)_u Step 6w + 5 Link

1(81)_w not divisible by 7 !

1(91)_w not divisible by 7 !

3(13)_w not divisible by 7 !

3(23)_w not divisible by 7 !

3(43)_w / 7 (34*10ⁿ–43)/(99*7) = [49](062049)_u Step 6w + 3 Link

3(53)_w not divisible by 7 !

3(73)_w / 7 (37*10ⁿ–73)/(99*3) = [5339](105339)_u Step 6w + 5 Link

3(83)_w not divisible by 7 !

7(17)_w / 7 (71*10ⁿ–17)/(99*7) = [1](024531)_u Step 6w + 1 Link

7(27)_w / 7 (72*10ⁿ–27)/(99*7) = [1](038961)_u Step 6w + 1 Link

7(37)_w / 7 (73*10ⁿ–37)/(99*7) = [1](053391)_u Step 6w + 1 Link

7(47)_w / 7 (74*10ⁿ–47)/(99*7) = [1](067821)_u Step 6w + 1 Link

7(57)_w / 7 (75*10ⁿ–57)/(99*7) = [1](082251)_u Step 6w + 1 Link

7(87)_w / 7 (78*10ⁿ–87)/(99*7) = [1](125541)_u Step 6w + 1 Link

7(97)_w / 7 (79*10ⁿ–97)/(99*7) = [1](139971)_u Step 6w + 1 Link

9(19)_w not divisible by 7 !

9(29)_w not divisible by 7 !

9(49)_w not divisible by 7 !

9(59)_w / 7 (95*10ⁿ–59)/(99*7) = [137](085137)_u Step 6w + 3 Link

9(79)_w / 7 (97*10ⁿ–79)/(99*7) = [13997](113997)_u Step 6w + 5 Link

9(89)_w not divisible by 7 !

Hereunder at the left you'll find the table with the files containing the primefactors of the SUP's (Smoothly Undulating Palindromes).
At the right you'll find the corresponding 6-digit NSUP's.

SUP (Smoothly Undulating Composite Palindromes) reference files

2(12)_w = (21*10ⁿ–12)/99 facsup212.htm (by P. De Geest).

2(32)_w = (23*10ⁿ–32)/99 facsup232.htm (by P. De Geest).

2(52)_w = (25*10ⁿ–52)/99 facsup252.htm (by P. De Geest).

2(72)_w = (27*10ⁿ–72)/99 facsup272.htm (by P. De Geest).

2(92)_w = (29*10ⁿ–92)/99 facsup292.htm (by P. De Geest).

4(14)_w = (41*10ⁿ–14)/99 facsup414.htm (by P. De Geest).

4(34)_w = (43*10ⁿ–34)/99 facsup434.htm (by P. De Geest).

4(54)_w = (45*10ⁿ–54)/99 facsup454.htm (by P. De Geest).

4(74)_w = (47*10ⁿ–74)/99 facsup474.htm (by P. De Geest).

4(94)_w = (49*10ⁿ–94)/99 facsup494.htm (by P. De Geest).

5(15)_w = (51*10ⁿ–15)/99 facsup515.htm (by P. De Geest).

5(25)_w = (52*10ⁿ–25)/99 facsup525.htm (by P. De Geest).

5(35)_w = (53*10ⁿ–35)/99 facsup535.htm (by P. De Geest).

5(45)_w = (54*10ⁿ–45)/99 facsup545.htm (by P. De Geest).

5(65)_w = (56*10ⁿ–65)/99 facsup565.htm (by P. De Geest).

5(75)_w = (57*10ⁿ–75)/99 facsup575.htm (by P. De Geest).

5(85)_w = (58*10ⁿ–85)/99 facsup585.htm (by P. De Geest).

5(95)_w = (59*10ⁿ–95)/99 facsup595.htm (by P. De Geest).

6(16)_w = (61*10ⁿ–16)/99 facsup616.htm (by P. De Geest).

6(56)_w = (65*10ⁿ–56)/99 facsup656.htm (by P. De Geest).

6(76)_w = (67*10ⁿ–76)/99 facsup676.htm (by P. De Geest).

7(67)_w = (76*10ⁿ–67)/99 facsup767.htm (by P. De Geest).

8(18)_w = (81*10ⁿ–18)/99 facsup818.htm (by P. De Geest).

8(38)_w = (83*10ⁿ–38)/99 facsup838.htm (by P. De Geest).

8(58)_w = (85*10ⁿ–58)/99 facsup858.htm (by P. De Geest).

8(78)_w = (87*10ⁿ–78)/99 facsup878.htm (by P. De Geest).

8(98)_w = (89*10ⁿ–98)/99 facsup898.htm (by P. De Geest).

[k](d₁d₂d₃d₄d₅d₆)_n = NSUP's (Near Smoothly Undulating Primes) Mark 3

2(12)_w not divisible by 3 !

2(32)_w / 2⁵ / 3 (23*10ⁿ–32)/(99*32*3) = [242](003367)_u Step 6w + 5 Link

2(52)_w Always Composite (Steps 6w + 3 always divisible by 7)

2(72)_w not divisible by 3 !

2(92)_w / 2² / 3 (29*10ⁿ–92)/(99*4*3) = [2441](077441)_u Step 6w + 5 Link

4(14)_w / 2 / 3 (41*10ⁿ–14)/(99*2*3) = [69](023569)_u Step 6w + 3 Link

4(34)_w / 2 / 3 (43*10ⁿ–34)/(99*2*3) = [7239](057239)_u Step 6w + 5 Link

4(54)_w not divisible by 3 !

4(74)_w / 2 / 3 (47*10ⁿ–74)/(99*2*3) = [79](124579)_u Step 6w + 3 Link

4(94)_w / 2 / 3 (49*10ⁿ–94)/(99*2*3) = [8249](158249)_u Step 6w + 5 Link

5(15)_w not divisible by 3 !

5(25)_w Always Composite (Steps 6w + 3 always divisible by 7)

5(35)_w / 5 / 3 (53*10ⁿ–35)/(99*5*3) = [3569](023569)_u Step 6w + 5 Link

5(45)_w not divisible by 3 !

5(65)_w / 5 / 3 (56*10ⁿ–65)/(99*5*3) = [3771](043771)_u Step 6w + 5 Link

5(75)_w not divisible by 3 !

5(85)_w Always Composite (Steps 6w + 3 always divisible by 13)

5(95)_w / 5 / 3 (59*10ⁿ–95)/(99*5*3) = [3973](063973)_u Step 6w + 5 Link

6(16)_w / 2⁴ / 3 (61*10ⁿ–16)/(99*16*3) = [128367](003367)_u Step 6w + 1 Link

6(56)_w / 2³ / 3 (65*10ⁿ–56)/(99*8*3) = [273569](023569)_u Step 6w + 1 Link

6(76)_w / 2² / 3 (67*10ⁿ–76)/(99*4*3) = [563973](063973)_u Step 6w + 1 Link

7(67)_w / 3 (76*10ⁿ–67)/(99*3) = [25589](225589)_u Step 6w + 5 Link

8(18)_w not divisible by 3 !

8(38)_w / 2 / 3 (83*10ⁿ–38)/(99*2*3) = [13973](063973)_u Step 6w + 5 Link

8(58)_w Always Composite (Steps 6w + 3 always divisible by 13)

8(78)_w not divisible by 3 !

8(98)_w / 2 / 3 (89*10ⁿ–98)/(99*2*3) = [14983](164983)_u Step 6w + 5 Link

[k](d₁d₂d₃d₄d₅d₆)_n = NSUP's (Near Smoothly Undulating Primes) Mark 7

2(12)_w not divisible by 7 !

2(32)_w not divisible by 7 !

2(52)_w / 2² / 3 / 7 (25*10ⁿ–52)/(99*4*3*7) = [3](006253)_u Step 6w + 3 Link

2(72)_w / 2³ / 7 (27*10ⁿ–72)/(99*8*7) = [487](012987)_u Step 6w + 5 Link

2(92)_w not divisible by 7 !

4(14)_w not divisible by 7 !

4(34)_w / 2 / 7 (43*10ⁿ–34)/(99*2*7) = [31](024531)_u Step 6w + 3 Link

4(54)_w not divisible by 7 !

4(74)_w / 2 / 7 (47*10ⁿ–74)/(99*2*7) = [3391](053391)_u Step 6w + 5 Link

4(94)_w not divisible by 7 !

5(15)_w not divisible by 7 !

5(25)_w / 3 / 5² / 7 (52*10ⁿ–25)/(99*25*3*7) = [1](000481)_u Step 6w + 3 Link

5(35)_w not divisible by 7 !

5(45)_w not divisible by 7 !

5(65)_w not divisible by 7 !

5(75)_w / 5² / 7 (57*10ⁿ–75)/(99*25*7) = [329](004329)_u Step 6w + 5 Link

5(85)_w not divisible by 7 !

5(95)_w / 5 / 7 (59*10ⁿ–95)/(99*5*7) = [17](027417)_u Step 6w + 3 Link

6(16)_w / 2⁴ / 7 (61*10ⁿ–16)/(99*16*7) = [5501443](001443)_u Step 6w + 9 Link

6(56)_w not divisible by 7 !

6(76)_w / 2² / 7 (67*10ⁿ–76)/(99*4*7) = [2417](027417)_u Step 6w + 5 Link

7(67)_w / 7 (76*10ⁿ–67)/(99*7) = [1](096681)_u Step 6w + 1 Link

8(18)_w not divisible by 7 !

8(38)_w not divisible by 7 !

8(58)_w not divisible by 7 !

8(78)_w / 2 / 7 (87*10ⁿ–78)/(99*2*7) = [6277](056277)_u Step 6w + 5 Link

8(98)_w not divisible by 7 !

Case [k](d₁d₂d₃d₄d₅d₆)_u = [prefix](6-digit undulator).
Attentive readers of the factor lists will have noticed with me that some SUP primefactors are themselves near smoothly undulating. 'Near' because of an initial prefix and the repeating 6-digit undulators.
This time we divide the SUP with some or all of its prime factors upto 13. The number of candidates for 'Mark 13' are significant lower than the previous ones (only 5 cases found) hence the following concise table.
'Mark 11' wasn't forgotten but yield only 22-digit undulators (For these cases with long undulators see undulmore.htm).

[k](d₁d₂d₃d₄d₅d₆)_n = NSUP's (Near Smoothly Undulating Primes)	Mark 13
4(94)_w / 2 / 13 (4910ⁿ–94)/(992*13) = [19](036519)_u	Step 6w + 3	Link
5(85)_w / 3 / 5 / 13 (5810ⁿ–85)/(993513) = [3](004403)_u	Step 6w + 3	Link
6(76)_w / 2² / 13 (6710ⁿ–76)/(994*13) = [13](014763)_u	Step 6w + 3	Link
7(67)_w / 13 (7610ⁿ–67)/(9913) = [59](052059)_u	Step 6w + 3	Link
8(58)_w / 2 / 3 / 13 (8510ⁿ–58)/(992313) = [11](007511)_u	Step 6w + 3	Link

The “NSUP” Table

The reference table for
Near Smoothly Undulating Primes
Cases with 6-digit undulators
derived from the SUPP's
  Mark 3

This collection is complete for
probable primes up to see headings digits.
PDG = Patrick De Geest

NSUP Formula
Accolades = prime exp Who When Status Prime
Certificat

¬
   n ⩾ 50141 (PDG, August 16, 2022)

1(31)₂₄₉₈/3 = [4377](104377)₈₃₂ (13*10⁴⁹⁹⁷–31)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 50655 (PDG, August 16, 2022)

1(41)₁/3 = [47](138047)₀ (14*10^{3}–41)/(99*3) PDG Aug 06 2022 PRP View

1(41)₁₉₉/3 = [47](138047)₆₆ (14*10³⁹⁹–41)/(99*3) PDG Aug 06 2022 PRP View

1(41)₁₆₆₅₄/3 = [47](138047)₅₅₅₁ (14*10³³³⁰⁹–41)/(99*3) PDG Aug 16 2022 PRP View

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   n ⩾ 51677 (PDG, August 17, 2022)

1(61)₂/3 = [5387](205387)₀ (16*10^{5}–61)/(99*3) PDG Aug 06 2022 PRP View

1(61)₂₀₆/3 = [5387](205387)₆₈ (16*10⁴¹³–61)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 50001 (PDG, August 7, 2022)

1(71)₈₅/3 = [57](239057)₂₈ (17*10¹⁷¹–71)/(99*3) PDG Aug 06 2022 PRP View

1(71)₂₀₂/3 = [57](239057)₆₇ (17*10⁴⁰⁵–71)/(99*3) PDG Aug 06 2022 PRP View

1(71)₅₂₆/3 = [57](239057)₁₇₅ (17*10¹⁰⁵³–71)/(99*3) PDG Aug 06 2022 PRP View

1(71)₄₇₇₇/3 = [57](239057)₁₅₉₂ (17*10⁹⁵⁵⁵–71)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 50009 (PDG, August 7, 2022)

1(91)₂/3 = [6397](306397)₀ (19*10^{5}–91)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 50095 (PDG, August 17, 2022)

3(13)₅₇/3 = [1](043771)₁₉ (31*10¹¹⁵–13)/(99*3) PDG Aug 06 2022 PRP View

3(13)₃₈₁/3 = [1](043771)₁₂₇ (31*10⁷⁶³–13)/(99*3) PDG Aug 06 2022 PRP View

3(13)₂₆₁₀/3 = [1](043771)₈₇₀ (31*10⁵²²¹–13)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 50161 (PDG, August 17, 2022)

3(23)₁₃₂/3 = [1](077441)₄₄ (32*10²⁶⁵–23)/(99*3) PDG Aug 06 2022 PRP View

3(23)₄₀₅₀/3 = [1](077441)₁₃₅₀ (32*10^{8101}–23)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 51433 (PDG, August 17, 2022)

3(43)₂₅₅/3 = [1](144781)₈₅ (34*10⁵¹¹–43)/(99*3) PDG Aug 06 2022 PRP View

3(43)₁₆₉₉₅/3 = [1](144781)₅₆₆₅ (34*10³³⁹⁹¹–43)/(99*3) PDG Aug 17 2022 PRP View

3(43)₂₁₁₉₈/3 = [1](144781)₇₀₆₆ (34*10^{42397}–43)/(99*3) PDG Aug 17 2022 PRP View

¬
   n ⩾ 51997 (PDG, August 17, 2022)

3(53)₆/3 = [1](178451)₂ (35*10^{13}–53)/(99*3) PDG Aug 06 2022 PRP View

3(53)₁₅/3 = [1](178451)₅ (35*10^{31}–53)/(99*3) PDG Aug 06 2022 PRP View

3(53)₈₇/3 = [1](178451)₂₉ (35*10¹⁷⁵–53)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 50101 (PDG, August 17, 2022)

3(73)₃/3 = [1](245791)₁ (37*10^{7}–73)/(99*3) PDG Aug 06 2022 PRP View

3(73)₁₂/3 = [1](245791)₄ (37*10²⁵–73)/(99*3) PDG Aug 06 2022 PRP View

3(73)₄₃₅/3 = [1](245791)₁₄₅ (37*10⁸⁷¹–73)/(99*3) PDG Aug 06 2022 PRP View

3(73)₄₆₂/3 = [1](245791)₁₅₄ (37*10⁹²⁵–73)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 53689 (PDG, August 18, 2022)

3(83)₆/3 = [1](279461)₂ (38*10^{13}–83)/(99*3) PDG Aug 06 2022 PRP View

3(83)₃₃/3 = [1](279461)₁₁ (38*10^{67}–83)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 53001 (PDG, August 18, 2022)

7(17)₁/3 = [239](057239)₀ (71*10^{3}–17)/(99*3) PDG Aug 06 2022 PRP View

7(17)₄₁₄₁/3 = [239](057239)₁₃₈₀ (71*10⁸²⁸³–17)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 50231 (PDG, August 18, 2022)

7(37)₂₆/3 = [24579](124579)₈ (73*10^{53}–37)/(99*3) PDG Aug 06 2022 PRP View

7(37)₂₀₇₇₁/3 = [24579](124579)₆₉₂₃ (73*10^{41543}–37)/(99*3) PDG Aug 18 2022 PRP View

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   n ⩾ 51705 (PDG, August 18, 2022)

7(47)₇/3 = [24579](124579)₂ (74*10¹⁵–47)/(99*3) PDG Aug 06 2022 PRP View

7(47)₅₁₃₇/3 = [24579](124579)₁₇₁₂ (74*10¹⁰²⁷⁵–47)/(99*3) PDG Aug 06 2022 PRP View

7(47)₅₁₈₈/3 = [24579](124579)₁₇₂₉ (74*10¹⁰³⁷⁷–47)/(99*3) PDG Aug 06 2022 PRP View

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   n ⩾ 50315 (PDG, August 19, 2022)

7(97)₁₃₆₁/3 = [26599](326599)₄₅₃ (79*10²⁷²³–97)/(99*3) PDG Aug 06 2022 PRP View

7(97)₁₁₇₁₄/3 = [26599](326599)₃₉₀₄ (79*10²³⁴²⁹–97)/(99*3) PDG Aug 19 2022 PRP View

7(97)₁₆₇₀₆/3 = [26599](326599)₅₅₆₈ (79*10^{33413}–97)/(99*3) PDG Aug 19 2022 PRP View

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   n ⩾ 50353 (PDG, August 19, 2022)

9(19)₀/3 = [3](063973)₀ (91*10¹–19)/(99*3) PDG Aug 06 2022 PRP View

9(19)₂₇₄₈/3 = [3](063973)₉₁₆ (91*10⁵⁴⁹⁷–19)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 51289 (PDG, August 19, 2022)

9(29)₀/3 = [3](097643)₀ (92*10¹–29)/(99*3) PDG Aug 06 2022 PRP View

9(29)₁₄₁/3 = [3](097643)₄₇ (92*10^{283}–29)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 50071 (PDG, August 19, 2022)

9(49)₀/3 = [3](164983)₀ (94*10¹–49)/(99*3) PDG Aug 06 2022 PRP View

9(49)₃/3 = [3](164983)₁ (94*10^{7}–49)/(99*3) PDG Aug 06 2022 PRP View

9(49)₅₅₄₇/3 = [3](164983)₁₈₄₉ (94*10¹¹⁰⁹⁵–49)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 58615 (PDG, August 20, 2022)

9(59)₀/3 = [3](198653)₀ (95*10¹–59)/(99*3) PDG Aug 06 2022 PRP View

9(59)₃/3 = [3](198653)₁ (95*10^{7}–59)/(99*3) PDG Aug 06 2022 PRP View

9(59)₁₂/3 = [3](198653)₄ (95*10²⁵–59)/(99*3) PDG Aug 06 2022 PRP View

9(59)₈₄/3 = [3](198653)₂₈ (95*10¹⁶⁹–59)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 52375 (PDG, August 20, 2022)

9(79)₀/3 = [3](265993)₀ (97*10¹–79)/(99*3) PDG Aug 06 2022 PRP View

9(79)₃/3 = [3](265993)₁ (97*10^{7}–79)/(99*3) PDG Aug 06 2022 PRP View

9(79)₂₄/3 = [3](265993)₈ (97*10⁴⁹–79)/(99*3) PDG Aug 06 2022 PRP View

9(79)₄₂/3 = [3](265993)₁₄ (97*10⁸⁵–79)/(99*3) PDG Aug 06 2022 PRP View

9(79)₁₀₂₃/3 = [3](265993)₃₄₁ (97*10²⁰⁴⁷–79)/(99*3) PDG Aug 06 2022 PRP View

9(79)₂₀₄₀/3 = [3](265993)₆₈₀ (97*10⁴⁰⁸¹–79)/(99*3) PDG Aug 06 2022 PRP View

¬
   n ⩾ 51079 (PDG, August 20, 2022)

9(89)₀/3 = [3](299663)₀ (98*10¹–89)/(99*3) PDG Aug 06 2022 PRP View

9(89)₆/3 = [3](299663)₂ (98*10^{13}–89)/(99*3) PDG Aug 06 2022 PRP View

9(89)₉₇₅/3 = [3](299663)₃₂₅ (98*10^{1951}–89)/(99*3) PDG Aug 06 2022 PRP View

The reference table for
Near Smoothly Undulating Primes
Cases with 6-digit undulators
derived from the composite set of SUP's
  Mark 3

This collection is complete for
probable primes up to see headings digits.
PDG = Patrick De Geest

NSUP Formula
Accolades = prime exp Who When Status Prime
Certificat

¬
   n ⩾ 53855 (PDG, August 21, 2022)

2(32)₄₇₀₆/2⁵/3 = [242](003367)₁₅₆₈ (23*10^{9413}–32)/(99*32*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 50063 (PDG, August 21, 2022)

2(92)₂/2²/3 = [2441](077441)₀ (29*10^{5}–92)/(99*4*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 50067 (PDG, August 21, 2022)

4(14)₇/2/3 = [69](023569)₂ (41*10¹⁵–14)/(99*2*3) PDG Aug 09 2022 PRP View

4(14)₂₅₀/2/3 = [69](023569)₈₃ (41*10⁵⁰¹–14)/(99*2*3) PDG Aug 09 2022 PRP View

4(14)₂₆₇₆/2/3 = [69](023569)₈₉₀ (41*10⁵³⁴³–14)/(99*2*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 72305 (PDG, August 21, 2022)

4(34)₁₄₃/2/3 = [7239](057239)₄₇ (43*10²⁸⁷–34)/(99*2*3) PDG Aug 09 2022 PRP View

4(34)₇₁₀₉/2/3 = [7239](057239)₂₃₆₉ (43*10¹⁴²¹⁹–34)/(99*2*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 53325 (PDG, August 22, 2022)

4(74)₁/2/3 = [79](124579)₀ (47*10^{3}–74)/(99*2*3) PDG Aug 09 2022 PRP View

4(74)₂₂₆/2/3 = [79](124579)₇₅ (47*10⁴⁵³–74)/(99*2*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 52259 (PDG, August 22, 2022)

4(94)₅₉/2/3 = [8249](158249)₁₉ (49*10¹¹⁹–94)/(99*2*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 50729 (PDG, August 10, 2022)

5(35)₃₅/5/3 = [3569](023569)₁₁ (53*10^{71}–35)/(99*5*3) PDG Aug 09 2022 PRP View

5(35)₂₁₈/5/3 = [3569](023569)₇₂ (53*10⁴³⁷–35)/(99*5*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 50609 (PDG, August 22, 2022)

5(65)₃₂/5/3 = [3771](043771)₁₀ (56*10⁶⁵–65)/(99*5*3) PDG Aug 09 2022 PRP View

5(65)₁₆₄₆/5/3 = [3771](043771)₅₄₈ (56*10³²⁹³–65)/(99*5*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 67655 (PDG, August 23, 2022)

5(95)₂₀/5/3 = [3973](063973)₆ (59*10^{41}–95)/(99*5*3) PDG Aug 09 2022 PRP View

5(95)₆₉₅/5/3 = [3973](063973)₂₃₁ (59*10¹³⁹¹–95)/(99*5*3) PDG Aug 09 2022 PRP View

¬
   n ⩾ 80047 (PDG, August 12, 2022)

6(16)_?/2⁴/3 = [128367](003367)_? (61*10^?–16)/(99*16*3) PDG Aug 11 2022 PRP View

¬
   n ⩾ 65935 (PDG, August 23, 2022)

6(56)₃/2³/3 = [273569](023569)₀ (65*10^{7}–56)/(99*8*3) PDG Aug 11 2022 PRP View

6(56)₇₄₂₅/2³/3 = [273569](023569)₂₄₇₄ (65*10^{14851}–56)/(99*8*3) PDG Aug 11 2022 PRP View

¬
   n ⩾ 50035 (PDG, August 11, 2022)

6(76)₉/2²/3 = [563973](063973)₂₄₇₄ (67*10^{19}–76)/(99*4*3) PDG Aug 11 2022 PRP View

6(76)₁₁₉₇₉/2²/3 = [563973](063973)₃₉₉₂ (67*10²³⁹⁵⁹–76)/(99*4*3) PDG Aug 11 2022 PRP View

¬
   n ⩾ 53951 (PDG, August 23, 2022)

7(67)₂/3 = [25589](225589)₀ (76*10^{5}–67)/(99*3) PDG Aug 11 2022 PRP View

7(67)₂₉/3 = [25589](225589)₉ (76*10^{59}–67)/(99*3) PDG Aug 11 2022 PRP View

¬
   n ⩾ 53213 (PDG, August 24, 2022)

8(38)₁₁/2/3 = [13973](063973)₃ (83*10^{23}–38)/(99*2*3) PDG Aug 11 2022 PRP View

8(38)₁₀₇/2/3 = [13973](063973)₃₅ (83*10²¹⁵–38)/(99*2*3) PDG Aug 11 2022 PRP View

8(38)₁₆₁/2/3 = [13973](063973)₅₃ (83*10³²³–38)/(99*2*3) PDG Aug 11 2022 PRP View

8(38)₃₈₉/2/3 = [13973](063973)₁₂₉ (83*10⁷⁷⁹–38)/(99*2*3) PDG Aug 11 2022 PRP View

¬
   n ⩾ 52385 (PDG, August 24, 2022)

8(98)₂/2/3 = [14983](164983)₀ (89*10^{5}–98)/(99*2*3) PDG Aug 11 2022 PRP View

8(98)₃₂₁₈/2/3 = [14983](164983)₁₀₇₂ (89*10^{6437}–98)/(99*2*3) PDG Aug 11 2022 PRP View

The reference table for
Near Smoothly Undulating Primes
Cases with 6-digit undulators
derived from the composite set of SUPP's
  Mark 7

This collection is complete for
probable primes up to see headings digits.
PDG = Patrick De Geest

NSUP Formula
Accolades = prime exp Who When Status Prime
Certificat

¬
   n ⩾ 51003 (PDG, August 24, 2022)

1(61)₄₀/7 = [23](088023)₁₃ (16*10⁸¹–61)/(99*7) PDG Aug 12 2022 PRP View

1(61)₁₆₀/7 = [23](088023)₅₃ (16*10³²¹–61)/(99*7) PDG Aug 12 2022 PRP View

1(61)₁₉₀/7 = [23](088023)₆₃ (16*10³⁸¹–61)/(99*7) PDG Aug 12 2022 PRP View

1(61)₄₄₂/7 = [23](088023)₁₄₇ (16*10⁸⁸⁵–61)/(99*7) PDG Aug 12 2022 PRP View

1(61)₅₁₁/7 = [23](088023)₁₇₀ (16*10¹⁰²³–61)/(99*7) PDG Aug 12 2022 PRP View

¬
   n ⩾ 51359 (PDG, August 12, 2022)

1(71)_?/7 = [2453](102453)_? (17*10^?–71)/(99*7) PDG Aug 12 2022 PRP View

¬
   n ⩾ 50031 (PDG, August 25, 2022)

3(43)₇₉/7 = [49](062049)₂₆ (34*10¹⁵⁹–43)/(99*7) PDG Aug 12 2022 PRP View

3(43)₂₈₀₉/7 = [49](062049)₉₃₆ (34*10⁵⁶¹⁹–43)/(99*7) PDG Aug 12 2022 PRP View

¬
   n ⩾ 54083 (PDG, August 12, 2022)

3(73)₁₂₃₀/7 = [5339](105339)₄₁₀ (37*10²⁴⁶⁵–73)/(99*7) PDG Aug 12 2022 PRP View

¬
   n ⩾ 52381 (PDG, August 25, 2022)

7(17)₂₁/7 = [1](024531)₇ (71*10^{43}–17)/(99*7) PDG Aug 12 2022 PRP View

7(17)₂₄/7 = [1](024531)₈ (71*10⁴⁹–17)/(99*7) PDG Aug 12 2022 PRP View

¬
   n ⩾ 53947 (PDG, August 25, 2022)

7(27)₉/7 = [1](038961)₃ (72*10^{19}–27)/(99*7) PDG Aug 12 2022 PRP View

7(27)₃₃/7 = [1](038961)₁₁ (72*10^{67}–27)/(99*7) PDG Aug 12 2022 PRP View

7(27)₈₄/7 = [1](038961)₂₈ (72*10¹⁶⁹–27)/(99*7) PDG Aug 12 2022 PRP View

7(27)₁₁₄/7 = [1](038961)₃₈ (72*10^{229}–27)/(99*7) PDG Aug 12 2022 PRP View

7(27)₁₈₀/7 = [1](038961)₆₀ (72*10³⁶¹–27)/(99*7) PDG Aug 12 2022 PRP View

7(27)₁₀₈₅₁/7 = [1](038961)₃₆₁₇ (72*10²¹⁷⁰³–27)/(99*7) PDG Aug 12 2022 PRP View

¬
   n ⩾ 51139 (PDG, August 26, 2022)

7(37)_?/7 = [1](053391)_? (73*10^?–37)/(99*7) PDG Aug 13 2022 PRP View

¬
   n ⩾ 50473 (PDG, August 26, 2022)

7(47)₆/7 = [1](067821)₂ (74*10^{13}–47)/(99*7) PDG Aug 13 2022 PRP View

7(47)₉/7 = [1](067821)₃ (74*10^{19}–47)/(99*7) PDG Aug 13 2022 PRP View

7(47)₁₈₃/7 = [1](067821)₆₁ (74*10^{367}–47)/(99*7) PDG Aug 13 2022 PRP View

¬
   n ⩾ 54451 (PDG, August 26, 2022)

7(57)₂₇₆₀/7 = [1](082251)₉₂₀ (75*10^{5521}–57)/(99*7) PDG Aug 13 2022 PRP View

7(57)₅₉₀₄/7 = [1](082251)₁₉₆₈ (75*10¹¹⁸⁰⁹–57)/(99*7) PDG Aug 13 2022 PRP View

¬
   n ⩾ 54901 (PDG, August 27, 2022)

7(87)₉/7 = [1](125541)₃ (78*10^{19}–87)/(99*7) PDG Aug 13 2022 PRP View

7(87)₆₀₀/7 = [1](125541)₂₀₀ (78*10^{1201}–87)/(99*7) PDG Aug 13 2022 PRP View

7(87)₁₅₀₉/7 = [1](125541)₅₀₃ (78*10^{3019}–87)/(99*7) PDG Aug 13 2022 PRP View

¬
   n ⩾ 53881 (PDG, August 27, 2022)

7(97)₁₂/7 = [1](139971)₄ (79*10²⁵–97)/(99*7) PDG Aug 13 2022 PRP View

7(97)₆₄₃₈/7 = [1](139971)₂₁₄₆ (79*10¹²⁸⁷⁷–97)/(99*7) PDG Aug 13 2022 PRP View

¬
   n ⩾ 52167 (PDG, August 27, 2022)

9(59)₇/7 = [137](085137)₂ (95*10¹⁵–59)/(99*7) PDG Aug 13 2022 PRP View

9(59)₇₉/7 = [137](085137)₂₆ (95*10¹⁵⁹–59)/(99*7) PDG Aug 13 2022 PRP View

9(59)₂₀₂/7 = [137](085137)₆₇ (95*10⁴⁰⁵–59)/(99*7) PDG Aug 13 2022 PRP View

9(59)₇₉₂₄/7 = [137](085137)₂₆₄₁ (95*10¹⁵⁸⁴⁹–59)/(99*7) PDG Aug 13 2022 PRP View

¬
   n ⩾ 50189 (PDG, August 27, 2022)

9(79)₂/7 = [13997](113997)₀ (97*10^{5}–79)/(99*7) PDG Aug 13 2022 PRP View

9(79)₈/7 = [13997](113997)₂ (97*10^{17}–79)/(99*7) PDG Aug 13 2022 PRP View

9(79)₃₇₈₂/7 = [13997](113997)₁₂₆₀ (97*10⁷⁵⁶⁵–79)/(99*7) PDG Aug 13 2022 PRP View

9(79)₅₃₂₁/7 = [13997](113997)₁₇₇₃ (97*10¹⁰⁶⁴³–79)/(99*7) PDG Aug 13 2022 PRP View

The reference table for
Near Smoothly Undulating Primes
Cases with 6-digit undulators
derived from the composite set of SUP's
  Mark 7

This collection is complete for
probable primes up to see headings digits.
PDG = Patrick De Geest

NSUP Formula
Accolades = prime exp Who When Status Prime
Certificat

¬
   n ⩾ 54015 (PDG, August 27, 2022)

2(52)₁/4/3/7 = [3](006253)₀ (25*10^{3}–52)/(99*4*3*7) PDG Aug 14 2022 PRP View

2(52)₁₇₂₆/4/3/7 = [3](006253)₅₇₅ (25*10³⁴⁵³–52)/(99*4*3*7) PDG Aug 14 2022 PRP View

¬
   n ⩾ 55145 (PDG, August 27, 2022)

2(72)₂/2³/7 = [487](012987)₀ (27*10^{5}–72)/(99*8*7) PDG Aug 14 2022 PRP View

2(72)₃₂/2³/7 = [487](012987)₁₀ (27*10⁶⁵–72)/(99*8*7) PDG Aug 14 2022 PRP View

2(72)₄₄₀/2³/7 = [487](012987)₁₄₆ (27*10^{881}–72)/(99*8*7) PDG Aug 14 2022 PRP View

2(72)₁₃₂₈/2³/7 = [487](012987)₄₄₂ (27*10^{2657}–72)/(99*8*7) PDG Aug 14 2022 PRP View

¬
   n ⩾ 51465 (PDG, August 28, 2022)

4(34)₁/2/7 = [31](024531)₀ (43*10^{3}–34)/(99*2*7) PDG Aug 14 2022 PRP View

4(34)₄/2/7 = [31](024531)₄₅ (43*10⁹–34)/(99*2*7) PDG Aug 14 2022 PRP View

4(34)₂₂/2/7 = [31](024531)₇ (43*10⁴⁵–34)/(99*2*7) PDG Aug 14 2022 PRP View

4(34)₄₃/2/7 = [31](024531)₁₄ (43*10⁸⁷–34)/(99*2*7) PDG Aug 14 2022 PRP View

4(34)₁₉₃/2/7 = [31](024531)₆₄ (43*10³⁸⁷–34)/(99*2*7) PDG Aug 14 2022 PRP View

4(34)₆₆₇₀/2/7 = [31](024531)₂₂₂₃ (43*10¹³³⁴¹–34)/(99*2*7) PDG Aug 14 2022 PRP View

¬
   n ⩾ 53261 (PDG, August 28, 2022)

4(74)₂/2/7 = [3391](053391)₀ (47*10^{5}–74)/(99*2*7) PDG Aug 14 2022 PRP View

4(74)₁₁/2/7 = [3391](053391)₃ (47*10^{23}–74)/(99*2*7) PDG Aug 14 2022 PRP View

4(74)₄₁/2/7 = [3391](053391)₁₃ (47*10^{83}–74)/(99*2*7) PDG Aug 14 2022 PRP View

4(74)₂₂₄/2/7 = [3391](053391)₇₄ (47*10^{449}–74)/(99*2*7) PDG Aug 14 2022 PRP View

4(74)₁₆₃₇/2/7 = [3391](053391)₅₄₅ (47*10³²⁷⁵–74)/(99*2*7) PDG Aug 14 2022 PRP View

¬
   n ⩾ 51195 (PDG, August 28, 2022)

5(25)₁/5²/3/7 = [1](000481)₀ (52*10^{3}–25)/(99*25*3*7) PDG Aug 14 2022 PRP View

5(25)₁₀/5²/3/7 = [1](000481)₃ (52*10²¹–25)/(99*25*3*7) PDG Aug 14 2022 PRP View

5(25)₄₀/5²/3/7 = [1](000481)₁₃ (52*10⁸¹–25)/(99*25*3*7) PDG Aug 14 2022 PRP View

5(25)₂₁₉₆₄/5²/3/7 = [1](000481)₇₃₂₁ (52*10⁴³⁹²⁹–25)/(99*25*3*7) PDG Aug 28 2022 PRP View

¬
   n ⩾ 51677 (PDG, August 28, 2022)

5(75)₁₁/5²/7 = [329](004329)₃ (57*10^{23}–75)/(99*25*7) PDG Aug 14 2022 PRP View

5(75)₂₆/5²/7 = [329](004329)₈ (57*10^{53}–75)/(99*25*7) PDG Aug 14 2022 PRP View

5(75)₄₂₈/5²/7 = [329](004329)₁₄₂ (57*10^{857}–75)/(99*25*7) PDG Aug 14 2022 PRP View

5(75)₆₄₄/5²/7 = [329](004329)₂₁₄ (57*10^{1289}–75)/(99*25*7) PDG Aug 28 2022 PRP View

¬
   n ⩾ 50127 (PDG, August 28, 2022)

5(95)₁/5/7 = [17](027417)₀ (59*10^{3}–95)/(99*5*7) PDG Aug 14 2022 PRP View

5(95)₂₃₂/5/7 = [17](027417)₇₇ (59*10⁴⁶⁵–95)/(99*5*7) PDG Aug 14 2022 PRP View

5(95)₃₃₉₁/5/7 = [17](027417)₁₁₃₀ (59*10⁶⁷⁸³–95)/(99*5*7) PDG Aug 14 2022 PRP View

5(95)₂₀₇₉₁/5/7 = [17](027417)₆₉₃₀ (59*10⁴¹⁵⁸³–95)/(99*5*7) PDG Aug 28 2022 PRP View

¬
   n ⩾ 52089 (PDG, August 28, 2022)

6(16)₄/2⁴/7 = [5501443](001443)₀ (61*10⁹–16)/(99*16*7) PDG Aug 15 2022 PRP View

6(16)₁₀/2⁴/7 = [5501443](001443)₂ (61*10²¹–16)/(99*16*7) PDG Aug 15 2022 PRP View

¬
   n ⩾ 51365 (PDG, August 29, 2022)

6(76)₂/2²/7 = [2417](027417)₀ (67*10^{5}–76)/(99*4*7) PDG Aug 15 2022 PRP View

6(76)₈/2²/7 = [2417](027417)₂ (67*10^{17}–76)/(99*4*7) PDG Aug 15 2022 PRP View

6(76)₁₃₄/2²/7 = [2417](027417)₄₄ (67*10^{269}–76)/(99*4*7) PDG Aug 15 2022 PRP View

6(76)₁₇₁₂₃/2²/7 = [2417](027417)₅₇₀₇ (67*10³⁴²⁴⁷–76)/(99*4*7) PDG Aug 29 2022 PRP View

¬
   n ⩾ 52915 (PDG, August 29, 2022)

7(67)₈₄/7 = [1](096681)₂₈ (76*10¹⁶⁹–67)/(99*7) PDG Aug 15 2022 PRP View

7(67)₁₀₃₅/7 = [1](096681)₃₄₅ (76*10²⁰⁷¹–67)/(99*7) PDG Aug 15 2022 PRP View

7(67)₈₆₇₀/7 = [1](096681)₂₈₉₀ (76*10¹⁷³⁴¹–67)/(99*7) PDG Aug 15 2022 PRP View

¬
   n ⩾ 60029 (PDG, August 16, 2022)

8(78)₂/2/7 = [6277](056277)₀ (87*10^{5}–78)/(99*2*7) PDG Aug 15 2022 PRP View

The reference table for
Near Smoothly Undulating Primes
Cases with 6-digit undulators
derived from both sets of SUPP's and SUP's
  Mark 13

This collection is complete for
probable primes up to see headings digits.
PDG = Patrick De Geest

NSUP Formula
Accolades = prime exp Who When Status Prime
Certificat

¬
   n ⩾ 20175 (PDG, August 25, 2022)

4(94)₁/2/13 = [19](036519)₀ (49*10^{3}–94)/(99*2*13) PDG Aug 24 2022 PRP View

4(94)₄/2/13 = [19](036519)₁ (49*10⁹–94)/(99*2*13) PDG Aug 24 2022 PRP View

4(94)₇₆/2/13 = [19](036519)₂₅ (49*10¹⁵³–94)/(99*2*13) PDG Aug 24 2022 PRP View

¬
   n ⩾ 20427 (PDG, August 25, 2022)

5(85)₁/3/5/13 = [3](004403)₀ (58*10^{3}–58)/(99*3*5*13) PDG Aug 24 2022 PRP View

5(85)₄/3/5/13 = [3](004403)₁ (58*10⁹–58)/(99*3*5*13) PDG Aug 24 2022 PRP View

5(85)₇/3/5/13 = [3](004403)₂ (58*10¹⁵–58)/(99*3*5*13) PDG Aug 24 2022 PRP View

5(85)₃₅₈/3/5/13 = [3](004403)₁₁₉ (58*10⁷¹⁷–58)/(99*3*5*13) PDG Aug 24 2022 PRP View

5(85)₁₂₀₄/3/5/13 = [3](004403)₄₀₁ (58*10²⁴⁰⁹–58)/(99*3*5*13) PDG Aug 24 2022 PRP View

¬
   n ⩾ 20259 (PDG, August 25, 2022)

6(76)₁/2²/13 = [13](014763)₀ (67*10^{3}–76)/(99*4*13) PDG Aug 24 2022 PRP View

6(76)₄/2²/13 = [13](014763)₁ (67*10⁹–76)/(99*4*13) PDG Aug 24 2022 PRP View

6(76)₁₀/2²/13 = [13](014763)₃ (67*10²¹–76)/(99*4*13) PDG Aug 24 2022 PRP View

6(76)₁₇₈/2²/13 = [13](014763)₅₉ (67*10³⁵⁷–76)/(99*4*13) PDG Aug 24 2022 PRP View

6(76)₅₈₀/2²/13 = [13](014763)₁₉₃ (67*10¹¹⁶¹–76)/(99*4*13) PDG Aug 24 2022 PRP View

6(76)₂₈₅₁/2²/13 = [13](014763)₉₅₀ (67*10⁵⁷⁰³–76)/(99*4*13) PDG Aug 24 2022 PRP View

¬
   n ⩾ 20109 (PDG, August 25, 2022)

7(67)₁/13 = [59](052059)₀ (76*10^{3}–67)/(99*13) PDG Aug 24 2022 PRP View

7(67)₁₃/13 = [59](052059)₄ (76*10²⁷–67)/(99*13) PDG Aug 24 2022 PRP View

7(67)₃₄/13 = [59](052059)₁₁ (76*10⁶⁹–67)/(99*13) PDG Aug 24 2022 PRP View

7(67)₆₀₄/13 = [59](052059)₂₀₁ (76*10¹²⁰⁹–67)/(99*13) PDG Aug 24 2022 PRP View

7(67)₇₁₈/13 = [59](052059)₂₃₉ (76*10¹⁴³⁷–67)/(99*13) PDG Aug 24 2022 PRP View

7(67)₈₇₄/13 = [59](052059)₂₉₁ (76*10¹⁷⁴⁹–67)/(99*13) PDG Aug 24 2022 PRP View

¬
   n ⩾ 40035 (PDG, August 25, 2022)

8(58)₁/2/3/13 = [11](007511)₀ (85*10^{3}–58)/(99*2*3*13) PDG Aug 24 2022 PRP View

8(58)₁₀/2/3/13 = [11](007511)₃ (85*10²¹–58)/(99*2*3*13) PDG Aug 24 2022 PRP View

8(58)₁₃/2/3/13 = [11](007511)₄ (85*10²⁷–58)/(99*2*3*13) PDG Aug 24 2022 PRP View

8(58)₁₂₇₀₃/2/3/13 = [11](007511)₄₂₃₄ (85*10²⁵⁴⁰⁷–58)/(99*2*3*13) PDG Aug 25 2022 PRP View

Sources Revealed

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The reference table for Near Smoothly Undulating Primes Cases with 6-digit undulators derived from the SUPP's					Mark 3
This collection is complete for probable primes up to see headings digits.		PDG = Patrick De Geest
NSUP	Formula Accolades = prime exp	Who	When	Status	Prime Certificat
¬	n ⩾ 50141 (PDG, August 16, 2022)
1(31)₂₄₉₈/3 = [4377](104377)₈₃₂	(1310⁴⁹⁹⁷–31)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50655 (PDG, August 16, 2022)
1(41)₁/3 = [47](138047)₀	(1410^{3}–41)/(993)	PDG	Aug 06 2022	PRP	View
1(41)₁₉₉/3 = [47](138047)₆₆	(1410³⁹⁹–41)/(993)	PDG	Aug 06 2022	PRP	View
1(41)₁₆₆₅₄/3 = [47](138047)₅₅₅₁	(1410³³³⁰⁹–41)/(993)	PDG	Aug 16 2022	PRP	View
¬	n ⩾ 51677 (PDG, August 17, 2022)
1(61)₂/3 = [5387](205387)₀	(1610^{5}–61)/(993)	PDG	Aug 06 2022	PRP	View
1(61)₂₀₆/3 = [5387](205387)₆₈	(1610⁴¹³–61)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50001 (PDG, August 7, 2022)
1(71)₈₅/3 = [57](239057)₂₈	(1710¹⁷¹–71)/(993)	PDG	Aug 06 2022	PRP	View
1(71)₂₀₂/3 = [57](239057)₆₇	(1710⁴⁰⁵–71)/(993)	PDG	Aug 06 2022	PRP	View
1(71)₅₂₆/3 = [57](239057)₁₇₅	(1710¹⁰⁵³–71)/(993)	PDG	Aug 06 2022	PRP	View
1(71)₄₇₇₇/3 = [57](239057)₁₅₉₂	(1710⁹⁵⁵⁵–71)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50009 (PDG, August 7, 2022)
1(91)₂/3 = [6397](306397)₀	(1910^{5}–91)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50095 (PDG, August 17, 2022)
3(13)₅₇/3 = [1](043771)₁₉	(3110¹¹⁵–13)/(993)	PDG	Aug 06 2022	PRP	View
3(13)₃₈₁/3 = [1](043771)₁₂₇	(3110⁷⁶³–13)/(993)	PDG	Aug 06 2022	PRP	View
3(13)₂₆₁₀/3 = [1](043771)₈₇₀	(3110⁵²²¹–13)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50161 (PDG, August 17, 2022)
3(23)₁₃₂/3 = [1](077441)₄₄	(3210²⁶⁵–23)/(993)	PDG	Aug 06 2022	PRP	View
3(23)₄₀₅₀/3 = [1](077441)₁₃₅₀	(3210^{8101}–23)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 51433 (PDG, August 17, 2022)
3(43)₂₅₅/3 = [1](144781)₈₅	(3410⁵¹¹–43)/(993)	PDG	Aug 06 2022	PRP	View
3(43)₁₆₉₉₅/3 = [1](144781)₅₆₆₅	(3410³³⁹⁹¹–43)/(993)	PDG	Aug 17 2022	PRP	View
3(43)₂₁₁₉₈/3 = [1](144781)₇₀₆₆	(3410^{42397}–43)/(993)	PDG	Aug 17 2022	PRP	View
¬	n ⩾ 51997 (PDG, August 17, 2022)
3(53)₆/3 = [1](178451)₂	(3510^{13}–53)/(993)	PDG	Aug 06 2022	PRP	View
3(53)₁₅/3 = [1](178451)₅	(3510^{31}–53)/(993)	PDG	Aug 06 2022	PRP	View
3(53)₈₇/3 = [1](178451)₂₉	(3510¹⁷⁵–53)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50101 (PDG, August 17, 2022)
3(73)₃/3 = [1](245791)₁	(3710^{7}–73)/(993)	PDG	Aug 06 2022	PRP	View
3(73)₁₂/3 = [1](245791)₄	(3710²⁵–73)/(993)	PDG	Aug 06 2022	PRP	View
3(73)₄₃₅/3 = [1](245791)₁₄₅	(3710⁸⁷¹–73)/(993)	PDG	Aug 06 2022	PRP	View
3(73)₄₆₂/3 = [1](245791)₁₅₄	(3710⁹²⁵–73)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 53689 (PDG, August 18, 2022)
3(83)₆/3 = [1](279461)₂	(3810^{13}–83)/(993)	PDG	Aug 06 2022	PRP	View
3(83)₃₃/3 = [1](279461)₁₁	(3810^{67}–83)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 53001 (PDG, August 18, 2022)
7(17)₁/3 = [239](057239)₀	(7110^{3}–17)/(993)	PDG	Aug 06 2022	PRP	View
7(17)₄₁₄₁/3 = [239](057239)₁₃₈₀	(7110⁸²⁸³–17)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50231 (PDG, August 18, 2022)
7(37)₂₆/3 = [24579](124579)₈	(7310^{53}–37)/(993)	PDG	Aug 06 2022	PRP	View
7(37)₂₀₇₇₁/3 = [24579](124579)₆₉₂₃	(7310^{41543}–37)/(993)	PDG	Aug 18 2022	PRP	View
¬	n ⩾ 51705 (PDG, August 18, 2022)
7(47)₇/3 = [24579](124579)₂	(7410¹⁵–47)/(993)	PDG	Aug 06 2022	PRP	View
7(47)₅₁₃₇/3 = [24579](124579)₁₇₁₂	(7410¹⁰²⁷⁵–47)/(993)	PDG	Aug 06 2022	PRP	View
7(47)₅₁₈₈/3 = [24579](124579)₁₇₂₉	(7410¹⁰³⁷⁷–47)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50315 (PDG, August 19, 2022)
7(97)₁₃₆₁/3 = [26599](326599)₄₅₃	(7910²⁷²³–97)/(993)	PDG	Aug 06 2022	PRP	View
7(97)₁₁₇₁₄/3 = [26599](326599)₃₉₀₄	(7910²³⁴²⁹–97)/(993)	PDG	Aug 19 2022	PRP	View
7(97)₁₆₇₀₆/3 = [26599](326599)₅₅₆₈	(7910^{33413}–97)/(993)	PDG	Aug 19 2022	PRP	View
¬	n ⩾ 50353 (PDG, August 19, 2022)
9(19)₀/3 = [3](063973)₀	(9110¹–19)/(993)	PDG	Aug 06 2022	PRP	View
9(19)₂₇₄₈/3 = [3](063973)₉₁₆	(9110⁵⁴⁹⁷–19)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 51289 (PDG, August 19, 2022)
9(29)₀/3 = [3](097643)₀	(9210¹–29)/(993)	PDG	Aug 06 2022	PRP	View
9(29)₁₄₁/3 = [3](097643)₄₇	(9210^{283}–29)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 50071 (PDG, August 19, 2022)
9(49)₀/3 = [3](164983)₀	(9410¹–49)/(993)	PDG	Aug 06 2022	PRP	View
9(49)₃/3 = [3](164983)₁	(9410^{7}–49)/(993)	PDG	Aug 06 2022	PRP	View
9(49)₅₅₄₇/3 = [3](164983)₁₈₄₉	(9410¹¹⁰⁹⁵–49)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 58615 (PDG, August 20, 2022)
9(59)₀/3 = [3](198653)₀	(9510¹–59)/(993)	PDG	Aug 06 2022	PRP	View
9(59)₃/3 = [3](198653)₁	(9510^{7}–59)/(993)	PDG	Aug 06 2022	PRP	View
9(59)₁₂/3 = [3](198653)₄	(9510²⁵–59)/(993)	PDG	Aug 06 2022	PRP	View
9(59)₈₄/3 = [3](198653)₂₈	(9510¹⁶⁹–59)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 52375 (PDG, August 20, 2022)
9(79)₀/3 = [3](265993)₀	(9710¹–79)/(993)	PDG	Aug 06 2022	PRP	View
9(79)₃/3 = [3](265993)₁	(9710^{7}–79)/(993)	PDG	Aug 06 2022	PRP	View
9(79)₂₄/3 = [3](265993)₈	(9710⁴⁹–79)/(993)	PDG	Aug 06 2022	PRP	View
9(79)₄₂/3 = [3](265993)₁₄	(9710⁸⁵–79)/(993)	PDG	Aug 06 2022	PRP	View
9(79)₁₀₂₃/3 = [3](265993)₃₄₁	(9710²⁰⁴⁷–79)/(993)	PDG	Aug 06 2022	PRP	View
9(79)₂₀₄₀/3 = [3](265993)₆₈₀	(9710⁴⁰⁸¹–79)/(993)	PDG	Aug 06 2022	PRP	View
¬	n ⩾ 51079 (PDG, August 20, 2022)
9(89)₀/3 = [3](299663)₀	(9810¹–89)/(993)	PDG	Aug 06 2022	PRP	View
9(89)₆/3 = [3](299663)₂	(9810^{13}–89)/(993)	PDG	Aug 06 2022	PRP	View
9(89)₉₇₅/3 = [3](299663)₃₂₅	(9810^{1951}–89)/(993)	PDG	Aug 06 2022	PRP	View

The reference table for Near Smoothly Undulating Primes Cases with 6-digit undulators derived from the composite set of SUPP's					Mark 7
This collection is complete for probable primes up to see headings digits.		PDG = Patrick De Geest
NSUP	Formula Accolades = prime exp	Who	When	Status	Prime Certificat
¬	n ⩾ 51003 (PDG, August 24, 2022)
1(61)₄₀/7 = [23](088023)₁₃	(1610⁸¹–61)/(997)	PDG	Aug 12 2022	PRP	View
1(61)₁₆₀/7 = [23](088023)₅₃	(1610³²¹–61)/(997)	PDG	Aug 12 2022	PRP	View
1(61)₁₉₀/7 = [23](088023)₆₃	(1610³⁸¹–61)/(997)	PDG	Aug 12 2022	PRP	View
1(61)₄₄₂/7 = [23](088023)₁₄₇	(1610⁸⁸⁵–61)/(997)	PDG	Aug 12 2022	PRP	View
1(61)₅₁₁/7 = [23](088023)₁₇₀	(1610¹⁰²³–61)/(997)	PDG	Aug 12 2022	PRP	View
¬	n ⩾ 51359 (PDG, August 12, 2022)
1(71)_?/7 = [2453](102453)_?	(1710^?–71)/(997)	PDG	Aug 12 2022	PRP	View
¬	n ⩾ 50031 (PDG, August 25, 2022)
3(43)₇₉/7 = [49](062049)₂₆	(3410¹⁵⁹–43)/(997)	PDG	Aug 12 2022	PRP	View
3(43)₂₈₀₉/7 = [49](062049)₉₃₆	(3410⁵⁶¹⁹–43)/(997)	PDG	Aug 12 2022	PRP	View
¬	n ⩾ 54083 (PDG, August 12, 2022)
3(73)₁₂₃₀/7 = [5339](105339)₄₁₀	(3710²⁴⁶⁵–73)/(997)	PDG	Aug 12 2022	PRP	View
¬	n ⩾ 52381 (PDG, August 25, 2022)
7(17)₂₁/7 = [1](024531)₇	(7110^{43}–17)/(997)	PDG	Aug 12 2022	PRP	View
7(17)₂₄/7 = [1](024531)₈	(7110⁴⁹–17)/(997)	PDG	Aug 12 2022	PRP	View
¬	n ⩾ 53947 (PDG, August 25, 2022)
7(27)₉/7 = [1](038961)₃	(7210^{19}–27)/(997)	PDG	Aug 12 2022	PRP	View
7(27)₃₃/7 = [1](038961)₁₁	(7210^{67}–27)/(997)	PDG	Aug 12 2022	PRP	View
7(27)₈₄/7 = [1](038961)₂₈	(7210¹⁶⁹–27)/(997)	PDG	Aug 12 2022	PRP	View
7(27)₁₁₄/7 = [1](038961)₃₈	(7210^{229}–27)/(997)	PDG	Aug 12 2022	PRP	View
7(27)₁₈₀/7 = [1](038961)₆₀	(7210³⁶¹–27)/(997)	PDG	Aug 12 2022	PRP	View
7(27)₁₀₈₅₁/7 = [1](038961)₃₆₁₇	(7210²¹⁷⁰³–27)/(997)	PDG	Aug 12 2022	PRP	View
¬	n ⩾ 51139 (PDG, August 26, 2022)
7(37)_?/7 = [1](053391)_?	(7310^?–37)/(997)	PDG	Aug 13 2022	PRP	View
¬	n ⩾ 50473 (PDG, August 26, 2022)
7(47)₆/7 = [1](067821)₂	(7410^{13}–47)/(997)	PDG	Aug 13 2022	PRP	View
7(47)₉/7 = [1](067821)₃	(7410^{19}–47)/(997)	PDG	Aug 13 2022	PRP	View
7(47)₁₈₃/7 = [1](067821)₆₁	(7410^{367}–47)/(997)	PDG	Aug 13 2022	PRP	View
¬	n ⩾ 54451 (PDG, August 26, 2022)
7(57)₂₇₆₀/7 = [1](082251)₉₂₀	(7510^{5521}–57)/(997)	PDG	Aug 13 2022	PRP	View
7(57)₅₉₀₄/7 = [1](082251)₁₉₆₈	(7510¹¹⁸⁰⁹–57)/(997)	PDG	Aug 13 2022	PRP	View
¬	n ⩾ 54901 (PDG, August 27, 2022)
7(87)₉/7 = [1](125541)₃	(7810^{19}–87)/(997)	PDG	Aug 13 2022	PRP	View
7(87)₆₀₀/7 = [1](125541)₂₀₀	(7810^{1201}–87)/(997)	PDG	Aug 13 2022	PRP	View
7(87)₁₅₀₉/7 = [1](125541)₅₀₃	(7810^{3019}–87)/(997)	PDG	Aug 13 2022	PRP	View
¬	n ⩾ 53881 (PDG, August 27, 2022)
7(97)₁₂/7 = [1](139971)₄	(7910²⁵–97)/(997)	PDG	Aug 13 2022	PRP	View
7(97)₆₄₃₈/7 = [1](139971)₂₁₄₆	(7910¹²⁸⁷⁷–97)/(997)	PDG	Aug 13 2022	PRP	View
¬	n ⩾ 52167 (PDG, August 27, 2022)
9(59)₇/7 = [137](085137)₂	(9510¹⁵–59)/(997)	PDG	Aug 13 2022	PRP	View
9(59)₇₉/7 = [137](085137)₂₆	(9510¹⁵⁹–59)/(997)	PDG	Aug 13 2022	PRP	View
9(59)₂₀₂/7 = [137](085137)₆₇	(9510⁴⁰⁵–59)/(997)	PDG	Aug 13 2022	PRP	View
9(59)₇₉₂₄/7 = [137](085137)₂₆₄₁	(9510¹⁵⁸⁴⁹–59)/(997)	PDG	Aug 13 2022	PRP	View
¬	n ⩾ 50189 (PDG, August 27, 2022)
9(79)₂/7 = [13997](113997)₀	(9710^{5}–79)/(997)	PDG	Aug 13 2022	PRP	View
9(79)₈/7 = [13997](113997)₂	(9710^{17}–79)/(997)	PDG	Aug 13 2022	PRP	View
9(79)₃₇₈₂/7 = [13997](113997)₁₂₆₀	(9710⁷⁵⁶⁵–79)/(997)	PDG	Aug 13 2022	PRP	View
9(79)₅₃₂₁/7 = [13997](113997)₁₇₇₃	(9710¹⁰⁶⁴³–79)/(997)	PDG	Aug 13 2022	PRP	View