Hermann Stamm-Wilbrandt Hermann-SW
Hermann-SW
/ gps2svgs
Last active
March 23, 2026 12:14
Combine PARI/GP script Graphviz output for several input values as SVGs into single row HTML table
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| #!/bin/bash | |
| # gps2svgs psp2.gp 341 561 645 1105 1387 1729 1905 2047 > tst.html | |
| # shell checked | |
| # | |
| scr=$1;shift | |
| echo "<html><body><table border=1><tr>" | |
| for n in "$@"; do echo "<td>$(dot -Tsvg <(n=$n gp -q < "$scr"))</td>"; done | |
| echo "</tr></table></body></html>" |
Hermann-SW
/ S-Unit.sol.sage
Created
March 12, 2026 20:42
SageMath diophantine S-Unit solve example: error free after many iterations of Google Gemini; changed to ℚ and added generator output by me
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| # 1. Setup | |
| x = polygen(QQ, 'x') | |
| # K.<i> = NumberField(x^2 + 1) # ℚ(i) | |
| K.<i> = NumberField(x - 1) | |
| # Using this, the root a is just 1. This forces Sage to wrap the rational | |
| # numbers in a "NumberField object" which possesses the .S_unit_group() method. | |
| # | |
| S_list = K.primes_above(2) + K.primes_above(3) |
Hermann-SW
/ 23.gp
Last active
March 5, 2026 15:18
There are no further Carmichael numbers N=2^a*3^b+1 below 10^70 (than 1729=2^6*3^3+1 and 46656=2^6*3^6+1)
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| is_carmichael_minus_1(f)={ | |
| n=factorback(f)+1; | |
| v=[d+1|d<-divisors(n-1),n%(d+1)==0&&isprime(d+1)]; | |
| vecprod(v)==n; \\ Korselt's criterion | |
| } | |
| m=10^70; | |
| { | |
| for(a=1,oo, | |
| if(2^a<=m, |
Hermann-SW
/ Car_n-1_3_prime_factors.gp
Last active
March 10, 2026 22:44
Prime factorization of N-1 having exactly 3 prime factors, for Carchmichael numbers N ≤ 10^24
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| {[ [2, 4; 5, 1; 7, 1], | |
| [2, 4; 3, 1; 23, 1], | |
| [2, 5; 7, 1; 11, 1], | |
| [2, 3; 3, 3; 7, 2], | |
| [2, 2; 3, 2; 1777, 1], | |
| [2, 3; 3, 2; 1753, 1], | |
| [2, 4; 3, 3; 1733, 1], | |
| [2, 8; 3, 2; 433, 1], | |
| [2, 3; 3, 5; 557, 1], | |
| [2, 3; 3, 3; 23, 3], |
Hermann-SW
/ Car_3.343dd.gp
Last active
March 2, 2026 08:19
3 prime factor Charmichael number examples for roughly every 3 decimal digits up to 343
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| assert(b)=if(!(b),error()); | |
| factmul(f1,f2)=matreduce(matconcat([f1,f2]~)); | |
| factval(F)=vecprod([v[1]^v[2]|v<-F~]); | |
| {Redu=[0,25,0,25,110,291,51,146,131,511,111,95,1121,2685,820,12481,16175,1866, | |
| 4500,11525,8960,441,390,14796,1280,1651,1730,24140,21226,18555,43391,3716,2980, | |
| 46701,38580,15450,5560,19445,14376,83660,32560,7516,5060,23806,57806,44636, | |
| 28985,73445,60936,55146,91400,82190,54255,8016,25591,71945,259946,147035,11301, | |
| 3375,2371,18486,466191,436551,422806,6220,153406,493275,222755,1572896,453141, | |
| 5385,422511,663666,364225,84081,52590,916505,285466,827301,5671,137266,120160, |
Hermann-SW
/ 96522.gp
Created
February 24, 2026 20:42
@neptune's largest known 96,522 decimal digits 3-Carmichael number, with single random base verification
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| \\ @Neptune's largest known 3-Carmichael number (96522 decimal digits): | |
| \\ https://www.mersenneforum.org/node/22080/page3#post1066763 | |
| p = 3*(5752211*43#/2-1)^1069/2+1; | |
| q = 3*(5752211*43#/2-1)^1069+1; | |
| r = 3*((5752211*43#/2-1)^1069+(5752211*43#/2-1)^2138)/1050650772710+1; | |
| n = p*q*r; | |
| print(#digits(n)); | |
| n1 = (n-1)/gcd(n-1,p-1); |
Hermann-SW
/ 3710.gp
Last active
February 25, 2026 04:35
3710 decimal digits Carmichael number from 1989 Dubner paper table 1
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| \\ 3710 decimal digits Carmichael number from 1989 Dubner paper table 1: | |
| \\ https://www.ams.org/journals/mcom/1989-53-187/S0025-5718-1989-0969484-8/S0025-5718-1989-0969484-8.pdf | |
| \\ | |
| T=47#/2;A=41;C=141847;M=(T*C-1)^A/4;P=6*M+1;Q=12*M+1;X=123165;R=1+(P*Q-1)/X; | |
| N=P*Q*R; | |
| \\ known partial N-1 factorization: https://www.mersenneforum.org/node/1106127 | |
| {F=[2,41;3,1;11,1;13,1;19,1;29,1;31,1;37,1;41,2;43,1;47,1;59,41;79,41;83,1; | |
| 1709,1;3527,1;3691,1;16943,1;469793,41;1799411527,1;3463701403,1; | |
| 731646295847,1;9957992526379,41;677868618879887,1;278798236535678281,1; | |
| 61534897980248555544581,1;9929897004627382451681972907710143,1];} |
Hermann-SW
/ par2.gp
Created
February 16, 2026 14:16
Parallel determination of primitive root of n-th Euclid prime
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| check(En, n, phi, g, i)={ | |
| parfor(i=1, n, lift(Mod(g, En)^(phi / prime(i))) == 1, r, if(r, return(0))); | |
| 1 | |
| } | |
| euclid_prime_find_root(n) = { | |
| my(En = vecprod(primes(n)) + 1, phi = En - 1); | |
| for(g=2, En-1, | |
| if(lift(kronecker(g, En))==-1, |
Hermann-SW
/ seq.gp
Created
February 16, 2026 14:13
Sequential determination of primitive root of n-th Euclid prime
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| euclid_prime_find_root(n) = { | |
| my(En = vecprod(primes(n)) + 1, phi = En - 1); | |
| for(g=2, En-1, | |
| if(lift(kronecker(g, En))==-1, | |
| my(is_root = 1); | |
| for(i=1, n, | |
| if(lift(Mod(g, En)^(phi / prime(i))) == 1, | |
| is_root = 0; | |
| break; |
Hermann-SW
/ a11.3399714628553118047.gp
Created
January 16, 2026 16:54
Compute number of primes of form x^2 + x + A for x <= 10^11 (for Jacobson and Williams A = 3399714628553118047)
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| export(A=3399714628553118047); a(n)=parsum(k=0, 10^n, isprime(k^2+k+A)); | |
| default(threadsizemax,1000*10^6); \\ default 8MB was too small | |
| # | |
| print(a(11)); |
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