World!Of
Numbers		 HOME plate
WON |

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Border Probable Primes around
'Powers of Ten'
rood Border PRP's table (0-4999) rood Border PRP's table (5000-9999)
rood Border PRP's table (10000-99999)
rood comments

Border PRP's around 'Powers of Ten'
brown line
                    10^(x-1)                                                10^x
      x-1             B                          x                            B             x+1
 ————————————————————>O<—————————————————————————————————————————————————————>O<————————————————————
                 R                                                  R
 ---------------o-----D-----o-------------------------------------------o-----D-----o---------------
                 E                                             E
               -y     R    +y                                          -y     R    +y

Project Research

Probable primes of the form 10^x ± y.
(y = displacement from axis)

Borderprimes. Closest primes around axes 10^x.

deficient prp : displacement < exponent
efficient prp : displacement = exponent
sufficient prp : displacement > exponent

displacement +y < -y versus +y > -y (statistics)

Search for equal + and - values (equidistant).

PrimeForm/GW (PFGW) Program

[ Extracted from PFGW documentation A.1.]

PrimeForm/GW (PFGW) is a primality tester.
It tests whether or not a number is prime, or at least it tries to.
It is able to test any arbitrary number, though some faster then others.
About the name: PrimeForm speaks for itself, the GW comes from George
Woltman, the person who made the extremely fast modular code available
for this project (well he made it for Prime95, but allows us to use it ;)
It is a command line (DOS Box) utility. It is an 'Open Source' project,
and is ported to Win32, Unix, Linux, BeOS, and possibly other platforms.
The source code can be obtained at [after an initial subscription]:
 http://groups.yahoo.com/group/openpfgw/files/
The most current development version, and the release version of PFGW
for Win32 can be obtained at:
 http://groups.yahoo.com/group/primeform/files/
There are two mailing-lists concerned with PFGW:
 http://groups.yahoo.com/group/primeform/
  which is the "user's group"
and
 http://groups.yahoo.com/group/openpfgw/
  which is the "developer's group".

Motivation

Patrick De Geest (that's me) started to maintain this list already back
in 2004 when confronted with the submissions by Milton L. Brown
in H. Lifchitz's PRP Records table. I felt I needed a more systematic
approach, hence the creation of this collection. Recently Phil Carmody
asked the same after he noted MLB's nice pair 10^12990 + 11163 and
10^12991 + 11163 in Yahoo's PrimeNumbers e-mail discussion list,
read message #18229.

At the same time this is a nice application for PFGW a PrimeForm project
where lots of people can participate and contribute for a long time to come
dependent on how many free cpu cycles one has. Reserve a small or large
range and get the job done. Nevertheless one can join in for just one
borderprime as well. Future generations of primehunters might use this list
of prp's e.g. as a huge store of candidates to test for genuine prime.

Data material

The main table is in text format and the files to be consulted are called
borderprp(0-4999).txt
borderprp(5000-9999).txt
borderprp(10000-99999).txt

Sloane's OEIS sequences

A033873, A033874 and A038804

http://www.research.att.com/~njas/sequences/A033873
http://www.research.att.com/~njas/sequences/A033874
http://www.research.att.com/~njas/sequences/A038804
A003617 and A003618
http://www.research.att.com/~njas/sequences/A003617
http://www.research.att.com/~njas/sequences/A003618
A096548
http://www.research.att.com/~njas/sequences/A096548

Initials and abbreviations

DA= Dirk Augustin
DH= Daniel Heuer
HL= Henri Lifchitz
HR= Harald Ritter
JE= Jason Earls
JKA= Jens Kruse Andersen
LRP= Lelio R. Paula
MHW= Meng-Hsuan Wu
MLB= Milton L. Brown
PDG= Patrick De Geest
TA= Torbjörn Alm
TM= Thomas Masser

ps. borderprp < 10000 will not be copyrighted nor dated
as they are quite easy to reproduce.

tbv = to be verified
vb = verified by

Source material

10^n - 1 is always divisible by 3
http://www.research.att.com/~njas/sequences/A089675 Numbers n such that 10^n - 3 is a prime. [>26045]
10^n - 5 is always divisible by 5
10^n - 7 is always divisible by 3
http://www.research.att.com/~njas/sequences/A095714 Numbers n such that 10^n - 9 is a prime. [>16104]
http://www.research.att.com/~njas/sequences/A092767 Numbers n such that 10^n - 11 is a prime. [>16500]

http://www.worldofnumbers.com/deplat.htm#pdp101 Note on numbers of the form 10^n + 1.
http://www.research.att.com/~njas/sequences/A049054 Numbers n such that 10^n + 3 is a prime. [>17753]
10^n + 5 is always divisible by 5
http://www.research.att.com/~njas/sequences/A088274 Numbers n such that 10^n + 7 is a prime. [>21717]
http://www.research.att.com/~njas/sequences/A088275 Numbers n such that 10^n + 9 is a prime. [>39000 by DA]
10^n + 11 is always divisible by 3.

http://www.fortunecity.com/skyscraper/epson/276/pr1_10k.htm

Many solutions above 10000 were found and published in :
http://www.primenumbers.net/prptop/prptop.php
by Milton L. Brown and are recapitulated in the list...
... but need be doublechecked !!!
as some are not the smallest of length x+1 or the largest of length x.

See also WONPLATE 161 at http://www.worldofnumbers.com/em161.htm

Sample PFGW code used

ABC2 10^$b-$a // {number_primes,$b,1}
a:from 1 to 1000001 step 2
b:from 10290 to 10299

Save this text file e.g. as 'border.txt' and
then execute the following command line :

pfgw -f border.txt

look in pfgw.log for found prp's
look in pfgw_err.log for errors that occurred (very rare though)

Reserved ranges

Patrick De Geest

from 8200 to 8999
and some loose ends here and there

from 17000 to 17999 all +y displacements > 99 !

Happy prp hunting...

Largest gaps sorted by merit

How to calculate the merit of a gap ?

meritgapx
12,20739837014173
9,902759443331
9,7021326525938
9,69517568787
9,610595682692
9,457827003798
9,40723308610761
9,3731131085241
9,261689863235
9,0551321906340
8,928237841157
8,91421139910295
8,85920963210277
8,830414382038
8,2081297106863

Curios

Record displacement value

10^30999 + 349947 by PDG (+ 10 feb 2008)
ps. displacement +y equals this palindromic expression 3 * 38883 * 3
The palindromic midfactor is further divisible by 3 & 13!
Am I lucky or am I unlucky ...

Here is a nice list of what I called efficient prp's
where the displacement equals the exponent. The largest
(most by HL) values > 10000 still have to be verified.
Note that the below lists are incomplete and needs doublechecking.

10^3 – 3
10^23 – 23
10^171 – 171
10^903 – 903
10^48107 – 48107
10^48449 – 48449
10^60959 – 60959 (tbv)

10^1 + 1
10^451 + 451
10^13807 + 13807
10^23769 + 23769 
                    10^(x-1)                                                10^x
      x-1             B                          x                            B             x+1
 ————————————————————>O<—————————————————————————————————————————————————————>O<————————————————————
                 R                                                  R
 ---------------o-----D-----o-------------------------------------------o-----D-----o---------------
                 E                                             E
               -y     R    +y                                          -y     R    +y
It sometimes happens that the smallest and largest borderprp
of a certain length x have identical absolute displacement values.
Here is my list so far : 

10^47 + 33 and 10^48 – 33
10^362 + 471 and 10^363 – 471
10^482 + 177 and 10^483 – 177
It sometimes happens that the negative and positive displacements
from a common border 10^x are the same i.e., equidistant.
Here is my list so far : 

10^17 – 3 and 10^17 + 3
10^45 – 9 and 10^45 + 9
10^3175 – 13431 and 10^3175 + 13431
Same 'outerbounds'.

10^17 – 3 and 10^18 + 3
10^19 – 39 and 10^20 + 39
10^46 – 33 and 10^47 + 33
10^153 – 453 and 10^154 + 453
10^195 – 39 and 10^196 + 39
10^277 – 273 and 10^278 + 273
10^315 – 627 and 10^316 + 627
10^354 – 129 and 10^355 + 129
10^582 – 2277 and 10^583 + 2277
10^2024 – 6741 and 10^2025 + 6741
10^5500 – 1767 and 10^5501 + 1767
Identical displacements for consecutive values x

Three consecutives

10^1 – 3
10^2 – 3
10^3 – 3
10^0 + 1
10^1 + 1
10^2 + 1

10^65 + 49
10^66 + 49
10^67 + 49
Two consecutives

10^49 – 57
10^50 – 57

10^303 – 59
10^304 – 59

10^3144 – 531
10^3145 – 531
10^5 + 3
10^6 + 3

10^8 + 7
10^9 + 7

10^17 + 3
10^18 + 3

10^12990 + 11163
10^12991 + 11163

Messages, annotations, links, etc.

10^581 ± y curious 10^581 - 851 and 10^581 + 1581 !

10^663 ± y curious as only digits 3 & 6 occur ! 10^663 - 33 and 10^663 + 6333 and also the gap shares this property *6366.

10^999 ± y 10^999+7 and Titanix by MLB

10^3669 ± y discriminant -y = 9663 is 'reverse' of exponent 3669.

10^5020 ± y Prime Gap of 82794 by MLB

10^5028 ± y Prime Gap of 48116 by MLB

10^9999 ± y 10^9999 + 33603 is genuine prime http://www.worldofnumbers.com/em144.htm

10^10000 ± y 101 PRP Gaps by MLB

10^10087 ± y commented by MLB " This is an interesting prime, n'est ce pas 10^10087+10089,10088 "

10^10003 ± y (Erroneous) Prime Gap of 72580 by MLB

10^10294 ± y 10^10294 + 20491 note that exponent and displacement are anagrams of each other.

10^10702 ± y (Alleged) Prime gap of 364,188 by MLB

10^10781 ± y 10^10781 + 781 : note the doubling of numbers when split like 10^10|781+781 !

10^12000 ± y 10^12000+3213 and P=/= NP by MLB

10^12002 ± y Prime Number GAP of 123,380 by MLB

10^12012 ± y (Wrong) Prime GAP of 61946 by MLB

10^12990 ± y 10^12990 + 11163 http://groups.yahoo.com/group/primenumbers/message/18227
10^12991 ± y 10^12991 + 11163 http://groups.yahoo.com/group/primenumbers/message/18229

10^13000 ± y 10^13000+10029 by MLB

10^14173 ± y Prime Gap of 398,370 by MLB and verified by TA

10^16000 ± y 10^16000+23967 is PRP (but also +7749 !) by MLB

10^18000 ± y Prime Gap of 69438 by MLB

10^20000 ± y Prime Gap of 118576 and 10^20000 + 56149 by MLB

10^31001 ± y 10^31001+336963 is PRP by MLB

Palindromes with at least 5 digits

2924		-6209		+32323		*38532		+ 32323 is a SUPP
3059		-2531		+10801		*13332		+ palindromic
3497		-19071		+24763		*43834		* palindromic gap
4217		-14741		+11103		*25844		- palindromic
4224		-22949		+1293		*24242		* palindromic gap
4244		-15351		+15873		*31224		- palindromic
4264		-4157		+10701		*14858		+ palindromic
4279		-24033		+3039		*27072		* palindromic gap
4320		-17589		+10993		*28582		* palindromic gap
4461		-3833		+12921		*16754		+ palindromic
4512		-22229		+6553		*28782		* palindromic gap
4646		-1389		+20223		*21612		* palindromic gap
4882		-7559		+13431		*20990		+ palindromic
5022		-14571		+9061		*23632		* palindromic gap
5118		-13731		+7543		*21274		- palindromic
5166		-5367		+42607		*47974		* palindromic gap
5203		-12027		+11311		*23338		+ palindromic 
5206		-2337		+12721		*15058		+ palindromic
5227		-10001		+18373		*28374		- palindromic
5230		-8459		+15373		*23832		* palindromic gap
5253		-4251		+18171		*22422		* palindromic gap
5289		-38283		+919		*39202		- & + palindromic
5339		-7913		+10101		*18014		+ palindromic
5362		-14141		+15349		*29490		- palindromic
5458		-10901		+6427		*17328		- palindromic
5487		-15251		+13549		*28800		- palindromic
5505		-34097		+12421		*46518		+ palindromic
5631		-33933		+11343		*45276		- palindromic
5674		-21107		+35853		*56960		+ palindromic
5775		-31013		+1621		*32634		- palindromic
5894		-18441		+10401		*28842		+ palindromic
5926		-15651		+17761		*33412		- palindromic
6008		-36537		+12247		*48784		* palindromic gap
6011		-11211		+7897		*19108		- palindromic
6022		-11493		+9309		*20802		* palindromic gap
6062		-539		+27943		*28482		* palindromic gap
6088		-21251		+19291		*40542		+ palindromic
6101		-22691		+2761		*25452		* palindromic gap
6117		-10589		+11511		*22100		+ palindromic
6128		-24741		+12721		*37462		+ palindromic
6137		-6693		+15019		*21712		* palindromic gap
6175		-5489		+32023		*37512		+ palindromic
6181		-12039		+14041		*26080		+ palindromic
6278		-6753		+12721		*19474		+ palindromic
6358		-18581		+11277		*29858		- palindromic
6380		-17471		+24339		*41810		- palindromic
6414		-13631		+11911		*25542		- & + palindromic
6418		-13431		+6171		*19602		- palindromic
6480		-38283		+2007		*40290		- palindromic
6558		-21089		+38283		*59372		+ palindromic  
6559		-12021		+13951		*25972		- palindromic
6577		-17871		+7713		*25584		- palindromic
6633		-11811		+15073		*26884		- palindromic
6674		-1931		+18081		*20012		+ palindromic
6689		-11411		+1617		*13028		- palindromic
6725		-18381		+6181		*24562		- palindromic
6762		-90197		+31713		*121910		+ palindromic
6801		-21441		+5731		*27172		* palindromic gap
6811		-15449		+47277		*62726		* palindromic gap
6848		-18581		+13813		*32394		- palindromic
6855		-9737		+19291		*29028		+ palindromic
6923		-35147		+11211		*46358		+ palindromic
6931		-9423		+12721		*22144		+ palindromic
6951		-1821		+19291		*21112		+ palindromic & palindromic gap
6958		-12083		+11211		*23294		+ palindromic
6968		-10001		+6139		*16140		- palindromic
6974		-16761		+20191		*36952		- palindromic
7006		-15051		+4291		*19342		- palindromic
7069		-36957		+13231		*50188		+ palindromic
7088		-17571		+25479		*43050		- palindromic
7095		-10301		+2007		*12308		- palindromic
7164		-6531		+18921		*25452		* palindromic gap
7182		-30947		+19891		*50838		+ palindromic
7205		-1071		+18381		*19452		+ palindromic
7309		-11883		+10339		*22222		* palindromic gap
7385		-30003		+12901		*42904		- palindromic
7465		-36063		+5613		*41676		- palindromic
7586		-9261		+15991		*25252		* palindromic gap
7606		-9323		+33601		*42924		* palindromic gap
7615		-1997		+15351		*17348		+ palindromic
7657		-5313		+10101		*15414		+ palindromic
7690		-16161		+68511		*84672		- palindromic
7698		-14811		+9831		*24642		* palindromic gap
7725		-11711		+42367		*54078		- palindromic
7753		-3239		+17071		*20310		+ palindromic
7802		-29951		+10753		*40704		* palindromic gap
7855		-33059		+30303		*63362		+ palindromic
7907		-2151		+79467		*81618		* palindromic gap
7922		-31113		+13933		*45046		- palindromic
7924		-30369		+16461		*46830		+ palindromic
8002		-19353		+4479		*23832		* palindromic gap
8122		-3743		+16759		*20502		* palindromic gap
8128		-9563		+34171		*43734		* palindromic gap
8164		-27317		+13731		*41048		+ palindromic


10010		-28787		+32929		*61716		* palindromic gap
10013		-4383		+20059		*24442		* palindromic gap
10028		-16761		+109081		*125842		- palindromic
10096		-8489		+81009		*89498		* palindromic gap
10155		-77877		+471		*78348		- palindromic
10238		-21831		+10401		*32232		+ palindromic
10333		-1103		+70807		*71910		+ palindromic
10364		-17771		+49129		*66900		- palindromic
10398		-7791		+17151		*24942		* palindromic gap
10416		-25379		+39193		*64572		+ palindromic
10481		-57647		+9829		*67476		* palindromic gap
10499		-36009		+31213		*67222		+ palindromic
10541		-20001		+33333		*53334		+ palindromic
10624		-11303		+39193		*50496		+ palindromic
10642		-12021		+13521		*25542		- palindromic


11112		-37673		+1197		*38870		- palindromic
11839		-7131		+877		*8008		* palindromic gap
11916		-1511		+43743		*45254		* palindromic gap
11968		-11711		+25341		*37052		- palindromic
12801		-16461		+38323		*54784		- palindromic
12901		-10001		+33057		*43058		- palindromic
13367		-48723		+33633		*82356		+ palindromic
13708		-77877		+10623		*88500		- palindromic
14000		-13587		+27927		*41514		* palindromic gap
14003		-16739		+8103		*24842		* palindromic gap
14103		-12321		+4683		*17004		- palindromic
14994		-113379		+98689		*212068		+ palindromic
15202		-37073		+363		*37436		- & + palindromic
15402		-38283		+4827		*43110		- palindromic
15999		-35753		+9139		*44892		- palindromic
19200		-38883		+16161		*55044		- & + palindromic
21219		-15737		+19591		*35328		+ palindromic
21752		-16073		+51703		*67776		* palindromic gap
22163		-12093		+110011		*122104		+ record palindromic
25004		-12267		+76021		*88288		* palindromic gap

Palindromic curios

51		-323		+121		*444		- + * all palindromes
87		-273		+373		*646		+ * palindromic and 10^87+373 of palindromic length 88
180		-2183		+313		*2496		+ palindromic and 10^180+313 of palindromic length 181
384		-717		+171		*888		- + * all palindromes
5775		-31013		+1621		*32634		exponent and - are palindromic
7095		-10301		+2007		*12308		palindromic - found by DA in the year +

Repunits and repdigits with at least 3 digits

111		55-, 67-, 460+, 784+, 3248+, 5194+,
222		88*,
333		222-, 231+, 1130-, 2111+, 7046+, 7110+,
444		51*, 703*,
666		2300*,			* Number of the Beast. Beastly gap !
777		461+, 695-, 1013+, 1018-, 1289-, 1755-, 2961+, 5993-, 11801+,
888		384*, 963*, 1685*,
999		183+, 1077-, 2104+, 2946-, 4046-, 4430-, 10803+,
1111		731+, 1512+, 1787+, 2146+, 3987+, 4056+, 5296+,
2222		1000*, 2879*,
3333		3197+, 4213+, 7042+,
9999		5593+, 10525+,
22222		7309*,
33333		10541+,

Tautonyms

1010		998*,
1212		665*, 2008*, 4732*,
1313		1622-, 3848-, 3933-, 5528-,
1414		4752*,
1717		2204+, 3922+, 8150+,
1818		643*, 1069*, 1155*, 1688*,
1919		351-, 1796-, 2977-, 4887-,
2121		1832+, 2282+, 3058-, 4597-, 4658+, 4841-, 5623+,
2323		518+, 638+, 1286+, 2360+, 3574+, 4970+,
2424		601*,
2727		3359+, 3501+, 4773+, 7259+,
2828		379*,
2929		1563+, 2052+, 4497+, 5568+,
3131		1075-, 2158-, 4697-, 5545-, 5622-, 5765-,
3232		625*,
3434		690*, 1939*,
3636		1246*,
3737		7420-,
3838		2289*,
3939		1498+,
4040		721*, 6231*,
4141		1445+, 1533+, 10492+,
4242		2476*, 4492*,
4343		2746-, 4664-,
4848		574*, 1080*, 6218*,
5151		1925+, 5087+, 5360-,
5252		4567*,
5353		3131+,
5656		7072*,
5757		2062-, 3162-, 4478-, 4587+, 8130-,
5959		1472+, 1903+, 6934+,
6363		793-, 1756+, 2599+, 2966-, 4439+, 6522-,
6767		4298-,
6969		1623-, 3326-, 4052+, 7553+, 12953+,
7171		3153+,
7979		5196-,
8181		6586-, 10554+, 14263-,
8282		2652*, 4548*,
8484		2393*,
8686		3364*, 3765*,
8787		5668+, 6807+,
8989		5792+,
9090		2724*,
9292		2097*,
9898		3992*,
239239		35630+,

Exponent, -y and +y simultaneously prime

11		-23		+3		*26		(p-p+p) sum 37 is also prime
13		-29		+37		*66		(p-p+p) sum 79 is also prime
17		-3		+3		*6		(p-p+p) sum 23 is also prime
71		-53		+273		*326		(p-p+p) sum 397 is also prime
73		-149		+79		*228		(p-p+p)
109		-83		+457		*540		(p-p+p)
127		-71		+283		*354		(p-p+p)
137		-269		+283		*552		(p-p+p)
337		-683		+181		*864		(p-p+p) sum 1201 is also prime
491		-431		+1609		*2040		(p-p+p) sum 2531 is also prime
541		-1481		+733		*2214		(p-p+p)
599		-2339		+2161		*4500		(p-p+p) sum 5099 is also prime
673		-2381		+1291		*3672		(p-p+p)
761		-29		+1237		*1266		(p-p+p) sum 2027 is also prime
821		-2393		+241		*2634		(p-p+p)
859		-4019		+457		*4476		(p-p+p)
977		-941		+229		*1170		(p-p+p) 
991		-1061		+547		*1608		(p-p+p)
1049		-2633		+181		*2814		(p-p+p) sum 3863 is also prime
1117		-5441		+409		*5850		(p-p+p) sum 6967 is also prime
1291		-149		+283		*432		(p-p+p) 
1327		-2687		+163		*2850		(p-p+p) sum 4177 is also prime
1361		-233		+4099		*4332		(p-p+p) sum 5693 is also prime
1487		-2081		+4483		*6564		(p-p+p)
1607		-431		+6793		*7224		(p-p+p) sum 8831 is also prime
1759		-2063		+19		*2082		(p-p+p)
2039		-6029		+11887		*17916		(p-p+p)
2063		-4349		+19		*4368		(p-p+p)
2131		-137		+1021		*1158		(p-p+p)
2143		-6917		+811		*7728		(p-p+p) sum 9871 is also prime
2543		-1259		+409		*1668		(p-p+p) sum 4211 is also prime
2633		-6833		+883		*7716		(p-p+p)
2767		-809		+2137		*2946		(p-p+p)
2777		-4649		+1249		*5898		(p-p+p)
2789		-5879		+10399		*16278		(p-p+p)
2833		-26711		+2281		*28992		(p-p+p)
2903		-3989		+421		*4410		(p-p+p)
3001		-797		+5113		*5910		(p-p+p)
3301		-383		+9733		*10116		(p-p+p)
3333		-4583		+2659		*7242		LAST SCANNED FOR (P-P+P)

10061		-26813		+2617		*29430		(p-p+p)

Varia

135		-1463		+1143		*2606		first time both > 1000
387		-2909		+4449		*7358		* record value
568		-801		+501		*1302		* Slag van Vlaanderen (Battle of Flanders)
594		-11		+789		*800		* identical consecutive gaps see next
595		-503		+297		*800		* identical consecutive gaps see previous
756		-1713		+1711		*3424		near_equidistant displacements
787		-14397		+3171		*17568		- first time > 10000
844		-1241		+177		*1418		* first world war
967		-1269		+687		*1956		* PDG's birthyear 1956 is not that dull :-)
999		-6101		+7		*6108		+7 is proven prime by Titanix
1001		-3069		+9337		*12406		- came across repeat pattern '3069' in square !
1247		-10283		+10111		*20394		first time both > 10000
1956		-9459		+541		*10000		* PDG's birthyear 1956 gives a round gap of 10000 !
2742		-363		+6637		*7000		* gap is a rounded number
3531		-7029		+21549		*28578		10^x ± y with range x from 3531 to 4201 by Dirk Augustin 5 okt 2006
3669		-9663		+4059		*13722		displacement is reverse of exponent !
4202		-11361		+14913		*26274		10^x ± y with range x from 4202 to 4999 by Dirk Augustin 27 dec 2006
5500		-1767		+18373		*20140		10^x ± y with range x from 5500 to 6300 by Dirk Augustin 13 maa 2007
6043		-15119		+4881		*20000		* rounded gap
6464		-20691		+2691		*23382		- is expansion of + : 2691 and 2{0}691
6678		-9081		+919		*10000		* a second round gap of 10000 like with exponent 1956
7000		-20181		+4981		*25162		10^x ± y with range x from 7000 to 7200 by Dirk Augustin 13 maa 2007
7265		-6789		+18091		*24880		- ascending digits
7327		-13041		+10431		*23472		displacements are anagrams of each other : -13041 vs. +10431
7386		-1463		+14863		*16326		+ is expansion of - : 1463 and 14{8}63

9999		-11333		+33603		*44936		+33603 is genuine prime (next prp = +55377)
10002		-62057		+7341		*69398		DA (- 11 dec 2006 ) > -96191 by mlb
10003		-9489		+48967		*58456		DA (+ 03 aug 2006) < +63091 by mlb
10006		-7301		+4659		*11960		DA (- 12 dec 2006) > -7329 by mlb
10007		-19833		+9001		*28834		DA (- 12 dec 2006) > -22743 by mlb
10009		-3789		+45159		*48948		DA (+ 03 aug 2006) < +49521 by mlb
10010		-28787		+32929		*61716		DA (+ 03 aug 2006) < +59689 by mlb
10012		-1977		+44679		*46656		DA (+ 8 aug 2006) < +170781 by mlb
10013		-4383		+20059		*24442		DA (+ 5 aug 2006) < +29247 by mlb
10015		-17949		+36783		*54732		DA (+ 8 aug 2006) < +116961 by mlb
10020		-237		+16657		*16894		DA (+ 15 sep 2006) < +46291 by mlb
10022		-6569		+18843		*25412		DA (+ 15 sep 2006) < +52783 by mlb
10023		-31781		+6537		*38318		DA (+ 4 aug 2006) < +58333 by mlb
10025		-7067		+26323		*33390		DA (+ 8 aug 2006) < +105417 by mlb
10027		-29037		+49707		*78744		DA (+ 8 aug 2006) < +104749 by mlb
10028		-16761		+41911		*58672		DA (+ 8 aug 2006) < +109081 by mlb
10029		-3693		+62047		*65740		DA (+ 9 aug 2006) < +106123 by mlb
10030		-8951		+19713		*28664		DA (+ 7 aug 2006) < +101157 by mlb
10033		-2211		+30459		*32670		DA (+ 8 aug 2006) < +115821 by mlb
10096		-8489		+22533		*31022		DA (+ 8 aug 2006) < +81009 by mlb
10165		-6543		+2823		*9366		- descending digits
10172		-34697		+7711		*42408		PDG (- 8 jun 2007) > -43733 by mlb
10174		-33003		+7861		*40864		PDG (- 8 jun 2007) > -139377 by mlb
10181		-33797		+23329		*57126		PDG (- 10 jun 2007) > -99057 by mlb
10211		-18903		+65029		*83932		PDG (- 19 jun 2007) > -25521 by mlb
10213		-33917		+61327		*95244		PDG (- 19 jun 2007) > -66773 by mlb
10218		-48807		+7263		*56070		PDG (- 20 jun 2007) > -50729 by mlb
10222		-82437		+5781		*88218		PDG (- 21 jun 2007) > -103017 by mlb
10224		-9207		+7957		*17164		PDG (- 21 jun 2007) > -52301 by mlb
10225		-18317		+10009		*28326		PDG (- 21 jun 2007) > -63893 by mlb
10259		-18689		+18691		*37380		near equal equidistant displacements
10378		-5883		+8853		*14736		displacements are anagrams of each other : -5883 vs. +8853
10433		-21219		+957		*22176		PDG (- 17 sep 2007) > -21629 by mlb
10501		-21701		+30213		*56610		PDG (- 30 dec 2007) > -26397 by mlb
10543		-73451		+77943		*151394		PDG (+ 13 dec 2006) < +233677 by mlb
10702		-108911		+19483		*128394		JKA (+ 12/2005 tbv) < +255277 by mlb
11114		-6957		+66667		*73624		PDG (+ 23 mei 2007) visually pleasing digits 10^11114+66667
11956		-5817		+114139		*119956		Compare exponent 11956 with gap 11(9)956
12007		-12707		+8239		*20946		PDG (- 26 apr 2008) > -20627 by mlb
12010		-14423		+14419		*28842		near equal displacements 14423 and 14419
12011		-26159		+10839		*36998		PDG (- 26 apr 2008) > -116069 by mlb
12012		-1559		+30879		*32438		DA (+ 2 aug 2006) < +60387 by mlb
12913		-120993		+5887		*126880		PDG (+ 22 mei 2007) < +178449 by mlb
15000		-8621		+76291		*84912		PDG (+ 17 dec 2006) < +114229 by mlb
16000		-32961		+7749		*40710		DA (+ 2 aug 2006) < +23967 by mlb
16001		-4197		+3921		*8118		DA (+ 2 aug 2006) < +15757 by mlb
27003		-18123		+116961		*135084		PDG (+ 16 apr 2008) < +126331 by mlb
29020		-?		+867		*?		PDG (+ 8 maa 2008) < +29833 by mlb
49999		-?		+91701		*?		PDG (+ started 11 feb 2005, ended 1 mar 2005)
59999		-?		+65197		*?		PDG (+ started 14 mar 2005, ended 30 mar 2005)


Noticing many numbers with displacement 10203 !
	10^2237 - 10203
	10^6100 + 10203
	10^7554 + 10203
	10^7805 + 10203
	10^26645 + 10203

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