Hermann-SW’s gists

Hermann-SW / diophantine.primes.cdru.wl

Created April 26, 2026 20:15

Simplifying prime producing system of 14 diophantine equations on 26 variables for p=2

	#!/usr/bin/env wolframscript
	(*
	based on
	https://www.ericzheng.org/files/misc/prime.wl
	details
	https://www.ericzheng.org/thoughts/prime-polynomial.html
	https://www.ericzheng.org/files/pdf/prime.pdf
	*)
	eq1 = w z + h + j - q
	eq2 = (g k + g + k)(h + j) + h - z

Hermann-SW / subsetsuM.cpp

Created April 12, 2026 08:20

Determine the (only 5) Mersenne prime exponents that cannot be built as sum of previous Mersenne prime exponents

	/*
	f=subsetsuM
	g++ -O3 -Wall -pedantic -Wextra $f.cpp -o $f
	cpplint --filter=-legal/copyright,-build/namespaces $f.cpp
	cppcheck --enable=all --suppress=missingIncludeSystem $f.cpp --check-config
	*/
	#include <iostream>
	#include <cassert>
	#include <cinttypes>

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

	#!/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

	# 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)

	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

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

	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

	\\ @Neptune's largest known 3-Carmichael number (96522 decimal digits):
	\\ https://www.mersenneforum.org/node/22080/page3#post1066763

	p = 3(575221143#/2-1)^1069/2+1;
	q = 3(575221143#/2-1)^1069+1;
	r = 3((575221143#/2-1)^1069+(5752211*43#/2-1)^2138)/1050650772710+1;
	n = pqr;
	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

	\\ 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=(TC-1)^A/4;P=6M+1;Q=12M+1;X=123165;R=1+(PQ-1)/X;
	N=PQR;
	\\ 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

	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 Stamm-Wilbrandt Hermann-SW