While programing a comment lint for the new database system an old question has come up. In the past we have let "ECPP" be an archivable class. With some...
... As we recently witnessed. ... Is it a property of the number or the proof? If a property of the number, then ECPP and APRCL classes contain the same ...
please see OP: http://groups.yahoo.com/group/primenumbers/message/8856 I have tested 1<x<=10^11 (4,772,369,646 PrPs). Many thanks to Michael Angel who tested...
... Re: Table #48 in Beiler's book on "least exponents" i.e. ORDER of p, to any base, e.g. ORD4 (7) = 3 or 4^3 == is congruent to 1 MOD 7. Thus, 3 is the...
... You may wish to consider what the factoring community does in analgous cases. It's occasionally the case that a factorization is found by two methods...
Paul Leyland
pleyland@...
Jan 2, 2003 8:59 am
10605
A new version availible here http://217.35.81.229/gmp/prime1.15.tar.bz2 which corrects some minor bugs , thanks to Phil Carmody NOTE: This should still be...
... I'm curious if there's anything special about the ... I have also looked at these factors.. It seems and this is only a conjecture that Let a1<a2 then if...
... There are three kinds of bugs: 1) Bugs that can make a prime number be declared composite 2) Bugs that can make a composite number be declared prime 3)...
... The recently corrected bug was type 3 , although as it was rare it acted like type 1 ... No specific reason , except the usual bugs that are in any program...
... 1) ECPP is at present an archivable class, with a top-20. I believe that it should stay like this, with Chris trying to chase up the folk in Marcel's...
... Maybe Marcel could try to encourage his top-20 to contact Chris? Congrats to Jeff Heleen: http://www.ellipsa.net/pages/primotop20.html (10^4769 - 1) / 3 -...
http://listserv.nodak.edu/scripts/wa.exe?A2=ind0301&L=nmbrthry&P=R2 has an interesting variant on the Sierpinski problem from Sun Zhi-Wei (of Wall-Sun-Sun...
Comment: Since Payam's PrP 19249+2^551542 is effectively unprovable, Prof. Sun Zhi-Wei's appeal is essentially directed at SoB, telling them that if/when...
Hello all and happy New Year, Could someone tell me, please, if this "stands up"? All odd numbers of the form (a^2 + b^2) / 2 with both a and b being odd, that...
... (03:22) gp > (a^2+b^2)/2 - (((a+b)/2)^2+((a-b)/2)^2) %1 = 0 i.e. if n=(a^2+b^2)/2, then n=(((a+b)/2)^2+((a-b)/2)^2) Phil ===== The answer to life's mystery...
... It means I'm running The PARI Group's "gp" package at 3:22am. It's free, it's incredibly powerful, and it answers these kinds of questions without even...
... http://www.bookfinder.com/ has access to a wider selection of books, but with the drawback that you have to pay for them (which is after all what makes...
Briefly: forprime (p=1000000,1000500, ep=eulerphi((p-1)*(p+1));print1(ep":"ep/(p^2-1)*1.0",")) indicates 0.22~< phi(p^2-1)/(p^2-1) <~0.33 leading one to the...
... I don't see why your belief is justified based on a small sample and no analysis. Just because a function is bounded over a small range doesn't mean it...
Paul Leyland
pleyland@...
Jan 3, 2003 1:07 pm
10621
It was actually a fish for some voluntary labour. Pari chokes on primes>1000000, and I have no other means of performing such high powers tests that would be...
Has anyone heard of any conjectures similar to the following ones I have come up with? Conjecture: For real x>1 the smallest n such that there's always a prime...
... Use 'calc' instead. Or bc. Or the other 'calc'. Or use gp and use 'p=nextprime(p+1)' rather than 'forprime(p='. ... One of (p-1) and (p+1) is divisible by...
Jon Perry mistakenly claimed that ... Invoke it with -p10000000 to precompute primes to 10M. Limit is about 430M, as I recall, but then you need to allocate...
I am doing some timing tests in Maple in order to hunt down some bugs in its large-integer computation. It would be useful if I had primes close to 2^(2^n)...
I'm sure this must fall down - can someone confirm pointing out where? Cheers, David All primes of the form 4n+1 are the sum of two squares For every odd...
... bugs in ... close ... found ... primes. ... running PFGW -f ABC2file 2^(2^14)+2775 is 2-PRP! (1.480000 seconds) 2^(2^13)+897 is 2-PRP! (0.280000 seconds) ...
... I don't know any list which goes up to such high powers of 2. Heheh, 2^(2^9) I could give you a vast number of examples for. You could generate PRPs using...
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