loading...



















(19*10^3-91)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(19*10^3-91)/99 N=191 *** N is prime! Time: 0 sec
(19*10^33-91)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(19*10^33-91)/99 N=191919191919191919191919191919191 Factor: 2 divides N - 1 Factor: 2^3 divides N + 1 Factor: 3^2 divides N + 1 Factor: 5 divides N - 1 Factor: 17 divides N - 1 Factor: 19 divides N - 1 Factor: 73 divides N - 1 Factor: 101 divides N - 1 Factor: 137 divides N - 1 Factor: 353 divides N - 1 Factorization results: F1=0.3736 F2=0.0575 F1=1151707059190 F2=72 Pass: gcd(7^((N-1)/2) - 1, N) = 1: R20=91919191919191919189 Pass: 7^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=21 p=1 q=-5 R20=26376038612055532515 Pass: U{N+1} = 0 (mod N): d=21 p=1 q=-5 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=1 q=-5 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=3 q=-3 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=5 q=1 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=7 q=7 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=9 q=15 R20=0 Fail: gcd(U{(N+1)/3}, N) not = 1: d=21 p=11 q=25 R20=0 Pass: gcd(U{(N+1)/3}, N) = 1: d=21 p=13 q=37 R20=78009140328684360793 Pass: U{N+1} = 0 (mod N): d=21 p=13 q=37 R20=0 Fail: gcd(7^((N-1)/5) - 1, N) not = 1: R20=0 Pass: gcd(11^((N-1)/5) - 1, N) = 1: R20=10358570146130473031 Pass: 11^(N-1) = 1 (mod N): R20=1 Fail: gcd(11^((N-1)/17) - 1, N) not = 1: R20=0 Pass: gcd(19^((N-1)/17) - 1, N) = 1: R20=88838895293886896968 Pass: 19^(N-1) = 1 (mod N): R20=1 Fail: gcd(19^((N-1)/19) - 1, N) not = 1: R20=0 Pass: gcd(21^((N-1)/19) - 1, N) = 1: R20=99048144912474182054 Pass: 21^(N-1) = 1 (mod N): R20=1 Pass: gcd(21^((N-1)/73) - 1, N) = 1: R20=71209687951095689107 Pass: gcd(21^((N-1)/101) - 1, N) = 1: R20=96035659430404359367 Pass: gcd(21^((N-1)/137) - 1, N) = 1: R20=13510298031863525966 Pass: gcd(21^((N-1)/353) - 1, N) = 1: R20=89446720749656928717 BLS tests passed: F1=0.3736 F2=0.0575 Main divisor test: F1=0.3643 F2=0.0575 G=0.4218 S=0.0000 T=1 G=41461454130840 Main divisor test passed: 1/1 Final divisor test: F=0.3736 G=0.4218 H=1.1690 t=-1 a=1 Final divisor test passed: 3/3 r=3 i=0 *** N is prime! Time: 0 sec
(19*10^133-91)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(19*10^133-91)/99 N=1919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191 Factor: 2 divides N - 1 Factor: 2^3 divides N + 1 Factor: 3 divides N - 1 Factor: 5 divides N - 1 Factor: 7 divides N - 1 Factor: 11 divides N - 1 Factor: 13 divides N - 1 Factor: 19 divides N - 1 Factor: 23 divides N - 1 Factor: 37 divides N - 1 Factor: 67 divides N - 1 Factor: 89 divides N - 1 Factor: 101 divides N - 1 Factor: 223 divides N + 1 Factor: 1831 divides N + 1 Factor: 4093 divides N - 1 Factor: 8779 divides N - 1 Factor: 9901 divides N - 1 Factor: 21649 divides N - 1 Factorization results: F1=0.2295 F2=0.0492 F1=2252311067972520570043136338230 F2=3266504 Pass: gcd(3^((N-1)/2) - 1, N) = 1: R20=91919191919191919189 Pass: 3^(N-1) = 1 (mod N): R20=1 Pass: gcd(U{(N+1)/2}, N) = 1: d=41 p=1 q=-10 R20=71774152659364658572 Pass: U{N+1} = 0 (mod N): d=41 p=1 q=-10 R20=0 Pass: gcd(3^((N-1)/3) - 1, N) = 1: R20=47406537659379797866 Pass: gcd(3^((N-1)/5) - 1, N) = 1: R20=82395409438720707344 Pass: gcd(3^((N-1)/7) - 1, N) = 1: R20=4719368843926060968 Pass: gcd(3^((N-1)/11) - 1, N) = 1: R20=82739052390513370192 Pass: gcd(3^((N-1)/13) - 1, N) = 1: R20=76906924500374664120 Pass: gcd(3^((N-1)/19) - 1, N) = 1: R20=7583226591901405322 Pass: gcd(3^((N-1)/23) - 1, N) = 1: R20=99680878719481819730 Pass: gcd(3^((N-1)/37) - 1, N) = 1: R20=62503517590133322273 Pass: gcd(3^((N-1)/67) - 1, N) = 1: R20=15312952577673687447 Pass: gcd(3^((N-1)/89) - 1, N) = 1: R20=65024500347211732743 Pass: gcd(3^((N-1)/101) - 1, N) = 1: R20=14400049278577728544 Pass: gcd(U{(N+1)/223}, N) = 1: d=41 p=1 q=-10 R20=7399397430180807243 Pass: gcd(U{(N+1)/1831}, N) = 1: d=41 p=1 q=-10 R20=43924908629905895755 Pass: gcd(3^((N-1)/4093) - 1, N) = 1: R20=71143599287789608240 Pass: gcd(3^((N-1)/8779) - 1, N) = 1: R20=48378169639103894267 Pass: gcd(3^((N-1)/9901) - 1, N) = 1: R20=56650526386137093111 Pass: gcd(3^((N-1)/21649) - 1, N) = 1: R20=45295604329420034963 BLS tests passed: F1=0.2295 F2=0.0492 APRCL test T=2520 S=457381315934822105041754361217 APRCL main test (1) at level 5 for p=2 APRCL main test (1 2) done: p=2 q=3 k=1 g=2 h=1 R20=91919191919191919190 APRCL main test (1 3) done: p=2 q=5 k=2 g=2 h=2 R20=9090909090909090909 APRCL main test (1 4) done: p=2 q=7 k=1 g=3 h=1 R20=91919191919191919190 APRCL main test (1 5) done: p=2 q=13 k=2 g=2 h=2 R20=29639591178052716514 APRCL main test (1 6) done: p=2 q=11 k=1 g=2 h=1 R20=91919191919191919190 APRCL main test (1 7) done: p=2 q=31 k=1 g=3 h=0 R20=1 APRCL main test (1 8) done: p=2 q=61 k=2 g=2 h=2 R20=25392869843286397976 APRCL main test (1 9) done: p=2 q=19 k=1 g=2 h=1 R20=91919191919191919190 APRCL main test (1 10) done: p=2 q=37 k=2 g=2 h=2 R20=14671182238749806317 APRCL L_2 condition satisfied APRCL main test (1 11) done: p=2 q=181 k=2 g=2 h=3 R20=60609143848361210468 APRCL main test (1 12) done: p=2 q=29 k=2 g=2 h=0 R20=41893368885045460550 APRCL main test (1 13) done: p=2 q=43 k=1 g=3 h=1 R20=91919191919191919190 APRCL main test (1 14) done: p=2 q=71 k=1 g=7 h=1 R20=91919191919191919190 APRCL main test (1 15) done: p=2 q=127 k=1 g=3 h=1 R20=91919191919191919190 APRCL main test (1 16) done: p=2 q=211 k=1 g=2 h=0 R20=1 APRCL main test (1 17) done: p=2 q=421 k=2 g=2 h=2 R20=31851649346472778974 APRCL main test (1 18) done: p=2 q=631 k=1 g=3 h=0 R20=1 APRCL main test (1 19) done: p=2 q=41 k=3 g=6 h=3 R20=29562890529161311259 APRCL main test (1 20) done: p=2 q=73 k=3 g=5 h=0 R20=71094465208773721515 APRCL main test (1 21) done: p=2 q=281 k=3 g=3 h=6 R20=21705123406656264221 APRCL main test (1 22) done: p=2 q=2521 k=3 g=17 h=1 R20=2634532644156261749 APRCL tests for p=2 completed APRCL main test (2) at level 5 for p=3 APRCL L_3 condition satisfied APRCL main test (2 4) for p=3 q=7 not needed APRCL main test (2 5) for p=3 q=13 not needed APRCL main test (2 7) done: p=3 q=31 k=1 g=3 h=1 R20=1 APRCL main test (2 8) done: p=3 q=61 k=1 g=2 h=2 R20=91919191919191919188 APRCL main test (2 9) for p=3 q=19 not needed APRCL main test (2 10) for p=3 q=37 not needed APRCL main test (2 11) done: p=3 q=181 k=2 g=2 h=1 R20=47509596548209857446 APRCL main test (2 13) done: p=3 q=43 k=1 g=3 h=2 R20=91919191919191919188 APRCL main test (2 15) done: p=3 q=127 k=2 g=3 h=6 R20=95995411797714860732 APRCL main test (2 16) done: p=3 q=211 k=1 g=2 h=0 R20=2 APRCL main test (2 17) done: p=3 q=421 k=1 g=2 h=1 R20=1 APRCL main test (2 18) done: p=3 q=631 k=2 g=3 h=1 R20=73592352716252114636 APRCL main test (2 20) done: p=3 q=73 k=2 g=5 h=6 R20=64179526103893656414 APRCL main test (2 22) done: p=3 q=2521 k=2 g=17 h=2 R20=47359466174849716517 APRCL tests for p=3 completed APRCL main test (3) at level 5 for p=5 APRCL L_5 condition satisfied APRCL main test (3 6) for p=5 q=11 not needed APRCL main test (3 7) done: p=5 q=31 k=1 g=3 h=4 R20=91919191919191919184 APRCL main test (3 8) done: p=5 q=61 k=1 g=2 h=4 R20=91919191919191919184 APRCL main test (3 11) done: p=5 q=181 k=1 g=2 h=2 R20=1 APRCL main test (3 14) done: p=5 q=71 k=1 g=7 h=2 R20=1 APRCL main test (3 16) done: p=5 q=211 k=1 g=2 h=2 R20=1 APRCL main test (3 17) done: p=5 q=421 k=1 g=2 h=3 R20=1 APRCL main test (3 18) done: p=5 q=631 k=1 g=3 h=4 R20=91919191919191919184 APRCL main test (3 19) done: p=5 q=41 k=1 g=6 h=0 R20=4 APRCL main test (3 21) done: p=5 q=281 k=1 g=3 h=2 R20=1 APRCL main test (3 22) done: p=5 q=2521 k=1 g=17 h=0 R20=4 APRCL tests for p=5 completed APRCL main test (4) at level 5 for p=7 APRCL L_7 condition satisfied APRCL main test (4 12) done: p=7 q=29 k=1 g=2 h=2 R20=1 APRCL main test (4 13) done: p=7 q=43 k=1 g=3 h=1 R20=1 APRCL main test (4 14) done: p=7 q=71 k=1 g=7 h=0 R20=6 APRCL main test (4 15) done: p=7 q=127 k=1 g=3 h=4 R20=1 APRCL main test (4 16) done: p=7 q=211 k=1 g=2 h=1 R20=1 APRCL main test (4 17) done: p=7 q=421 k=1 g=2 h=2 R20=1 APRCL main test (4 18) done: p=7 q=631 k=1 g=3 h=2 R20=1 APRCL main test (4 21) done: p=7 q=281 k=1 g=3 h=0 R20=6 APRCL main test (4 22) done: p=7 q=2521 k=1 g=17 h=4 R20=1 APRCL tests for p=7 completed Main divisor test: F1=0.2272 F2=0.0492 G=0.5006 S=0.2242 T=2520 G=1682519046847585500741630139051992051853505608916157880388330359320 Main divisor test passed: 2520/2520 *** N is prime! Time: 2 sec
(19*10^1969-91)/99 *** VFYPR 1.13F F_max=100000 S_min=100000 h=0 a=0 C=0 J=0 D=0 N=(19*10^1969-91)/99 N=1919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191919191 Factor: 3 divides N - 1 Factor: 7 divides N - 1 Factor: 13 divides N - 1 Factor: 17 divides N - 1 Factor: 37 divides N - 1 Factor: 73 divides N - 1 Factor: 83 divides N - 1 Factor: 101 divides N - 1 Factor: 137 divides N - 1 Factor: 739 divides N - 1 Factor: 1231 divides N - 1 Factor: 2953 divides N - 1 Factor: 9901 divides N - 1 Factor: 68389 divides N - 1 Factor: 148339 divides N - 1 Factor: 538987 divides N - 1 Factor: 922993 divides N - 1 Factor: 1144393 divides N - 1 Factor: 1811791 divides N - 1 Factor: 5882353 divides N - 1 Factor: 16419517 divides N - 1 Factor: 99990001 divides N - 1 Factor: 121553521 divides N - 1 Factor: 6051298241 divides N - 1 Factor: 626920594693 divides N - 1 Factor: 48656086054529 divides N - 1 Factor: 51635353141921 divides N - 1 Factor: 3322692262850881 divides N - 1 Factor: 9999999900000001 divides N - 1 Factor: 2670502781396266997 divides N - 1 Factor: 9425856976319889649 divides N - 1 Factor: 3404193829806058997303 divides N - 1 Factor: 36637591407529194237097 divides N - 1 Factor: 216667590115007379484962361 divides N - 1 Factor: 201763709900322803748657942361 divides N - 1 Factor: 669995415570582921859463287135169 divides N - 1 Factor: 8414640003465161203119978906558054839526493 divides N - 1 Factor: 61051796035522969271171274876554178504544683763248923853725596423 divides N - 1 Factor: 1447745997018511893740076606031686237538345362413531560645573104006506749609 divides N - 1 Factor: 2245236606248397162554620353530247131809555439174332456262048578539955402631665831489925370072038825037489223972536291929859656473 divides N - 1 Factor: 2 divides N - 1 Factor: 2^3 divides N + 1 Factor: 5 divides N - 1 Factor: 19 divides N - 1 Factorization results: F1=0.3331 F2=0.0005 F1=43459014223554332846491609558974208455857326218076774609673118413330679006002546178699639139033195552478685862596083777330527841284151520233508218178253328203453985849761893701299353227666566057588175712850763926394950003148801615805130800143378339496973126373582274254845026582588913407548154360700188621559728047813871991589635048037971583960654744778438041973093808206772131716478426627552606326038793684776069430025490619838691525353134331016206341155265524241916043117576114061119048540808963204569264004071172737333635121822654317546754444393624513777813426313925056105444242081302035711968454891281135048053184578503323920531783421134612552194780430 F2=8 Fail: gcd(3^((N-1)/3) - 1, N) not = 1: R20=0 Fail: gcd(7^((N-1)/3) - 1, N) not = 1: R20=0 Pass: gcd(11^((N-1)/3) - 1, N) = 1: R20=87480734891129243784 Pass: 11^(N-1) = 1 (mod N): R20=1 Fail: gcd(11^((N-1)/7) - 1, N) not = 1: R20=0 Pass: gcd(15^((N-1)/7) - 1, N) = 1: R20=29399268650489415050 Pass: 15^(N-1) = 1 (mod N): R20=1 Pass: gcd(15^((N-1)/13) - 1, N) = 1: R20=89038676462212584048 Pass: gcd(15^((N-1)/17) - 1, N) = 1: R20=70939510545910936126 Pass: gcd(15^((N-1)/37) - 1, N) = 1: R20=17545646562231624078 Pass: gcd(15^((N-1)/73) - 1, N) = 1: R20=32762603402788861879 Pass: gcd(15^((N-1)/83) - 1, N) = 1: R20=18093341948840718666 Pass: gcd(15^((N-1)/101) - 1, N) = 1: R20=32917820823783707466 Pass: gcd(15^((N-1)/137) - 1, N) = 1: R20=74702781363880306882 Pass: gcd(15^((N-1)/739) - 1, N) = 1: R20=38092867398858228149 Pass: gcd(15^((N-1)/1231) - 1, N) = 1: R20=87071079660730459256 Pass: gcd(15^((N-1)/2953) - 1, N) = 1: R20=33078846983595695328 Pass: gcd(15^((N-1)/9901) - 1, N) = 1: R20=50608019702305744800 Pass: gcd(15^((N-1)/68389) - 1, N) = 1: R20=55918170588880043280 Pass: gcd(15^((N-1)/148339) - 1, N) = 1: R20=69410621169427757180 Pass: gcd(15^((N-1)/538987) - 1, N) = 1: R20=44766863195664715917 Pass: gcd(15^((N-1)/922993) - 1, N) = 1: R20=36503033636539714170 Pass: gcd(15^((N-1)/1144393) - 1, N) = 1: R20=24815414017227561881 Pass: gcd(15^((N-1)/1811791) - 1, N) = 1: R20=5868623555690177036 Pass: gcd(15^((N-1)/5882353) - 1, N) = 1: R20=49740971329253614132 Pass: gcd(15^((N-1)/16419517) - 1, N) = 1: R20=278876980487863072 Pass: gcd(15^((N-1)/99990001) - 1, N) = 1: R20=80842675627789845001 Pass: gcd(15^((N-1)/121553521) - 1, N) = 1: R20=82376470014262056017 Pass: gcd(15^((N-1)/6051298241) - 1, N) = 1: R20=72794166441880507928 Pass: gcd(15^((N-1)/626920594693) - 1, N) = 1: R20=9895524827276738666 Pass: gcd(15^((N-1)/48656086054529) - 1, N) = 1: R20=92616037528810720665 Pass: gcd(15^((N-1)/51635353141921) - 1, N) = 1: R20=84043617816928052712 Pass: gcd(15^((N-1)/3322692262850881) - 1, N) = 1: R20=67428740368657929747 Pass: gcd(15^((N-1)/9999999900000001) - 1, N) = 1: R20=29962334400389613752 Pass: gcd(15^((N-1)/2670502781396266997) - 1, N) = 1: R20=90772145988186290173 Pass: gcd(15^((N-1)/9425856976319889649) - 1, N) = 1: R20=83230461081054722256 Pass: gcd(15^((N-1)/3404193829806058997303) - 1, N) = 1: R20=31561570084643310702 Pass: gcd(15^((N-1)/36637591407529194237097) - 1, N) = 1: R20=3228154149382238544 Pass: gcd(15^((N-1)/216667590115007379484962361) - 1, N) = 1: R20=68258389239116875783 Pass: gcd(15^((N-1)/201763709900322803748657942361) - 1, N) = 1: R20=66605491183224416230 Pass: gcd(15^((N-1)/669995415570582921859463287135169) - 1, N) = 1: R20=21473315373154347966 Pass: gcd(15^((N-1)/8414640003465161203119978906558054839526493) - 1, N) = 1: R20=2798794833298099967 Pass: gcd(15^((N-1)/61051796035522969271171274876554178504544683763248923853725596423) - 1, N) = 1: R20=68045572777961129706 Pass: gcd(15^((N-1)/1447745997018511893740076606031686237538345362413531560645573104006506749609) - 1, N) = 1: R20=60681384187802424239 Pass: gcd(15^((N-1)/2245236606248397162554620353530247131809555439174332456262048578539955402631665831489925370072038825037489223972536291929859656473) - 1, N) = 1: R20=73801768716965614240 Pass: gcd(15^((N-1)/2) - 1, N) = 1: R20=91919191919191919189 Pass: gcd(U{(N+1)/2}, N) = 1: d=53 p=1 q=-13 R20=18698753165749890181 Pass: U{N+1} = 0 (mod N): d=53 p=1 q=-13 R20=0 Fail: gcd(15^((N-1)/5) - 1, N) not = 1: R20=0 Fail: gcd(19^((N-1)/5) - 1, N) not = 1: R20=0 Pass: gcd(23^((N-1)/5) - 1, N) = 1: R20=95736225772771818420 Pass: 23^(N-1) = 1 (mod N): R20=1 Pass: gcd(23^((N-1)/19) - 1, N) = 1: R20=83853282063399045257 BLS tests passed: F1=0.3331 F2=0.0005 Main divisor test: F1=0.3329 F2=0.0005 G=0.3334 S=0.0000 T=1 G=173836056894217331385966438235896833823429304872307098438692473653322716024010184714798556556132782209914743450384335109322111365136606080934032872713013312813815943399047574805197412910666264230352702851403055705579800012595206463220523200573513357987892505494329097019380106330355653630192617442800754486238912191255487966358540192151886335842618979113752167892375232827088526865913706510210425304155174739104277720101962479354766101412537324064825364621062096967664172470304456244476194163235852818277056016284690949334540487290617270187017777574498055111253705255700224421776968325208142847873819565124540192212738314013295682127133684538450208779121720 Main divisor test passed: 1/1 Final divisor test: F=0.3331 G=0.3334 H=0.9996 t=-1 a=3 Final divisor test passed: 7/7 r=7 i=0 *** N is prime! Time: 139 sec
(19*10^2335-91)/99 == ID:B265804CD9840 ============================================= PRIMO 0.1.0 - Primality Certificate Started 08.15.2001 10:23:02 PM Running time 114h 16mn 18s Candidate certified prime ================================================================= Proved prime with 'Primo' by Hans Rosenthal. The zipped file "191_1167.zip" is 558 KB. When unpacked the file "Primo-B265804CD9840-001.out" is 1292 KB and is available on demand by simple email request.