... Yes, and every Aleph-Null prime means an Aleph-Null *prime factor* for all the factor freaks out there :) Does this make you (the prime factor freaks...
Hello all, I have just uploaded APSieve v0.68 to primeform files folder in the "Sieving Programs" folder. The PRP testing code has been fixed. The problem...
Happy New Year to all, It's starting well for me: my computers did a good job during my break holidays and found the new 388847-digit prime 857678^65536+1. Did...
Hello Yves, Thank you Mr 'Euro' Gallot for a concise piece of information describing where computer primers are in the search for infinity. David, please say...
Hello, John McNamara has started a group called oneandthreearefourgroup to discuss Fibonacci and Lucas sequences. This is an important area for new number...
Hello, Of course I forgot to mention that the answer to the first question is to be found at this link. http://groups.yahoo.com/group/oneandthreearefourgroup/ ...
Euclid's formula concerning perfect numbers, progressively developed for all values of n -except 1- produces numbers whose last ciphers are cyclic: 6-6-8-0. ...
Yes Shane, yours was indeed a nice observation. The classic Lucas-Lehmer test for Mersennes uses the Lucas sequence with p=2, q=-2, d=p^2-4*q=12 (Ribenboim...
4652
Paul Leyland
pleyland@...
Jan 3, 2002 11:05 am
... Nice wit, David, but Romans used addition not Multiplication. Paul...
4653
Yves Gallot
galloty@...
Jan 3, 2002 11:41 am
... An accurate computation of large C(n) is not easy: I think that you used the formula C_n = Prod[p odd prime] (1 - a_p / p)/(1 - 1 / p) = Prod[p odd prime]...
Hello! There were more my messages about GF density some weeks ago. I try to show all ideas in this one. Let consider GF(n,b). Let N=2^n, q=2*k*N+1 is prime (k...
Hello, For some number theory research, I need a programming language supporting unlimited precision integers. It should run on Windows and the execution of...
A recent addition to http://groups.yahoo.com/group/primeform/files/GenLuc/luctop.txt benefitted from Satoshi Tomabechi's SNFS. ... was missing 80 digits to...
Hello! There are some questions about GF(n,b). 1) Why GFNSieve doesn't remove b's which are odd powers of even numbers (e.g., 216)? Why doesn't Proth...
4660
Yves Gallot
galloty@...
Jan 4, 2002 11:41 am
... The test was not implemented in GFNSieve or in Proth. I considered that the proportion of GFN, with b's which are odd powers, and which have no small...
4661
William F Sindelar
w_sindelar@...
Jan 4, 2002 6:05 pm
Hi Everybody I don’t have the programs that can manipulate huge integers so I’m stuck and burning with curiosity. Can anyone calculate the next term in the...
... The next two numbers in the first series are composite. 977530816197201697619 = 19*31*102181*526931*30824161 and 955566496615167328821993756200407115362019...
4663
Paul Leyland
pleyland@...
Jan 4, 2002 6:39 pm
... Nope. A slightly abridged screen shot follows. Paul [pleyland@cam-01-unx ecmgmp]$ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software...
It is not prime. PFGW Version 20010828.Win_Dev (Alpha software, 'caveat utilitor') 31265489219^2+3*31265489219+1: 977530816197201697619 and then: ...
4665
Ignacio Larrosa Ca...
ignacio.larrosa@...
Jan 4, 2002 6:44 pm
... From: "William F Sindelar" <w_sindelar@...> To: <primenumbers@yahoogroups.com> Sent: Friday, January 04, 2002 7:04 PM Subject: [PrimeNumbers] Is the...
If 2^p -1 is a prime, then the sum of powers (consisting of p elements) existing between 2^p-1 and 2^2(p-1), extremes included, is a perfect. Example: p=3;...
FILIPPO GIORDANO has merely restated http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX36.html It's a good job that copyright on the Elements has...
In a message dated 02/01/2002 08:31:16 GMT Standard Time, ... What's going on here is a special case of the following. Let q be any prime = 3 mod 4. (This...
PS: This _very_ old theorem has an impeccable European lineage. Euclid proved (Book IX, Proposition 36) that ... In symbols: N(p) = 2^(p-1)*M(p) is perfect if ...
