Please check out this logic, which I just sent to someone who claimed, off list, to be able to "prove" that N=n^2-2 is never 2-SPSP. ... Note that Paul...
I can see no good reason why N=n^2-2 should not be 2-PSP, eventually. Consider n=138019, giving N=p1*p2 with primes p1=14087, p2=1352257 and (p2-1)/(p1-1)=96. ...
... The off-line claimant might also be interested in: http://www.primepuzzles.net/puzzles/puzz_239.htm Still I can not see why there should not be a...
... M=[0,1;5,5];forstep(n=7,10^9,10,if(!isprime(n),if(trace(Mod(M,n)^(n))==5,print(gcd(trace(Mod(M,n)^((n-1)/(2^factor(n-1)[1,2]))),n))))) ... I am "bumping"...
Let M=Mod([P,Q;1,0],n) with |P|>1,|Q|>1 and gcd(P,Q,n)=1 If kronecker(P^2-4*Q,n)==-1 and trace(M^n)==P then factors can be found by taking sequential square...
... using an example "n" from David regarding another conjecture, with n=430093*6021289;P=228621468092;Q=5 I can't factor "n"... Paul -- thinking that P should...
... No root of M^(n-1) will do it, let alone your mere square roots: fordiv(n-1,d,if(gcd(trace(M^((n-1)/d)),n)!=1,print(d))) [the rest is silence] But of...
... \\ No hiding place with that wriggle: \\ CRT can produce prime values for the Lucas parameter P. P=251718139;Q=5;n=250951*4768051;M=Mod([P,-Q;1,0],n); ...
Wow! How close can you get.... http://primes.utm.edu/primes/page.php?id=77690 99712838^16384+1 is prime! http://primes.utm.edu/primes/page.php?id=77689 ...
From: "David Broadhurst" <d.broadhurst@...> ... I know - I nearly collided with my floor when I saw that yesterday. Remembering that only even bases are...
Hi all, David Broadhurst asked me to post my ideas or 'proof' to the list. First, I've had a brief interest in aspects of prime numbers recently, but after...
Hi, I have a couple of questions about PFGW (1.2 for Windows). I think that PFGW has the fastest modular exponentiation that I've come across. When it does a...
... The default is -b3 which takes the same time as any other base. However the switch is useful, when dealing with divisors of 3^n-1, which are notorious as...
Congrats to the Hungarian team for a SG pair at 51780 digits: http://primes.utm.edu/primes/page.php?id=77705 which beats greatly the previous record at 36523...
... Close? these differ by 339824732360714867235790653[...130849 digits...]9000805700878318378218946562 <grin> But as to how close can you get, the bases...
... So now both the twin and Sophie records belong to http://primes.utm.edu/bios/code.php?code=x24 ... Note that each is of the form k*11#*2^171959 +/- 1 ...
... and then [7, [63739]] to make the sequence 3, 3, 3, 75, 113, 2163, 63739 a[n] is smallest number such that (a+1)^(2^n)+1 and (a-1)^(2^n)+1 are both prime ...
Too busy at work to fully reply to these posts. However, I have CONJECTURED that for the subset of N=n^2-2, namely where n= 2^k +/- 1, there is no 2-PSP. I...
... According to Yves's tables, the sequence to n=10 is 3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571 [Anyone care to check, please?] It seems from ...
... a[12] is known: 3, 3, 3, 75, 113, 2163, 63739, 13221, 54809, 3656571, a[11], 125441 so a double-sieve for a[11] would be appreciated. Then we could try to...
... CONJECTURED that for the subset of N=n^2-2, namely where n= 2^k +/- 1, there is no 2-PSP. I THINK that I am close to a proof, and I'm still working on it...
... I did mean Euler's Legendre calculation, and not the Jacobi one. http://primes.utm.edu/glossary/page.php/LegendreSymbol.html ... Legendre also only allows...
... in apparent ignorance of the fact that /every/ odd integer is a quadratic residue modulo 2. (The margin is too large for the proof:-) As Chris said: it is...
... I did a quick and dirty hack, running David Underbakke's AthGFNsieve, with Phil's "Wide-Range-Math", on b^2048+1 for even b in [4M,10M] to the (shallow)...
... Rats! I think I lost a factor of 2 :-( Help please, some sane person like Phil or Jens: it now seems to me that I need 2*mu^2 lines, to give mu^2 possible...
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