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  • http://primes.utm.edu/primes/page.php?id=120169 http://primes.utm.edu/primes/page.php?id=120170 these tri-megaprimes are unlikely to be prime http://primes.utm.edu/primes/page.php?id=120171 is testable in a reasonable amount of time Paul
    paulunderwood@... Jul 30
  • To add to Jack's reply: https://en.wikipedia.org/wiki/Generalized_taxicab_number Paul
    paulunderwood@... Jul 29
  • Hot on the heels of the last one from November, Karsten Klopffleisch of PrimeGrid has found a new mega-prime, the largest to date found by PrimeGrid: 3*2^11731850-1 (3,531,640 decimal digits) http://primes.utm.edu/primes/page.php?id=119571 Paul
    paulunderwood@... Mar 18
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  • Generalizing: {tst(a,k)=local(n=a^2+k);Mod(Mod(1,n)*(L+a),L^2+1)^(n+1)==a^2+1;} Clearly gcd(a,k)==1 is needed and n==3 (mod 4) and a>1. In the light of n=32239;a=63;k=28270; I further stipulate gcd(k-1,a)==1, In order to overcome the n==3 (mod 4) limitation, I propose the following test: {tst(a,k,x)=local(n=a^2+k); a>1&&gcd(k-1,a)==1&&gcd(k,a)==1&&kronecker(x^2-4,n)==-1&& Mod(Mod(1...
    paulunderwood@... Feb 4
  • Somewhere in the ancient history of this list, David Broadhurst tested n=a^2+2 as an a-prp up to some limit without finding a counterexample. Absurdly, how about using n-1 as a base for a prp test for such an n? I am joking. But how about the following test for n with a=3 (mod 6): {tst(a)=local(n=a^2+2);Mod(Mod(1,n)*(L+a),L^2+1)^(n+1)==-1} can you find a counterexample? I have...
    paulunderwood@... Feb 3
  • For those of you who have not seen my latest paper, for a free pdf download of it please visit: http://www.mersenneforum.org/showpost.php?p=388342&postcount=1 Paul
    paulunderwood@... Nov 29, 2014
  • The linked paper seems to be a great way to compute a modulo inverse, an improvement over the traditional extended Euclid algorithm: http://arxiv.org/abs/1408.4638 Paul
    paulunderwood@... Aug 21, 2014
  • Looking at the table on primesieve - Fast prime number generator primesieve - Fast prime number generator primesieve is a free software program and C/C++ library that generates primes using a highly optimized sieve of Eratosthenes implementation. View on primesieve.org Preview by Yahoo for 2^32 or 203,280,221 primes which would supposedly fir on your 2 bits per prime CD. CD? Did...
    paulunderwood@... Aug 4, 2014
  • Where the kronecker and gcd conditions are met, here is a 8 selfridge test for n coprime to 30: {ferfro(x,n)=gcd(x^3-x,n)==1&&kronecker(x^2-4,n)==-1&& Mod(2*x,n)^(n-1)==1&&Mod(Mod(1,n)*(L+x),L^2-x*L+1)^(n+1)==1+2*x^2;} {tst(n,x,y)=gcd(x^2-y^2,n)==1&&ferfro(x,n)&&ferfro(y,n);} I have verified this for n < 10^7. Can you find a pseudoprime for this test? Paul
    paulunderwood@... Aug 2, 2014
  • For the record: ----- -------------------------------- ------ ---- ---- -------------- rank description digits who year comment ----- -------------------------------- ------ ---- ---- -------------- 1 2^57885161-1 17425170 G13 2013 Mersenne 48?? 2 2^43112609-1 12978189 G10 2008 Mersenne 47?? 3 2^42643801-1 12837064 G12 2009 Mersenne 46?? 4 2^37156667-1 11185272 G11 2008 Mersenne 45...
    paulunderwood@... Jul 24, 2014