http://primes.utm.edu/primes/page.php?id=85584 is currently ploughing through the BLS tests for Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) which has 28.125%...
It seems to me that Boris Iskra's prime 3^534827-3^267414+1 in http://primes.utm.edu/primes/page.php?id=76301 is the "Generalized unique" record holder, at...
... I'm glad that I said that it was a weak argument, since PFGW found that (4358^4357-1)/4357^2 is Fermat and Lucas PRP! This is a probable prime whose...
... It might be useful if I confessed where my weak heuristic argument came from. It rested on these rather frail foundations: 1) I supposed that for prime p...
Various people asked me, off list, where this conjecture comes from. I obtained it by taking an 8th root of unity in a strong Frobenius test with fundamental...
... Do you actually want to PRP-test 80+ million bit integers, or do something else (say just remove small factors)? If the former, do you have the slightest...
After six months, my effort to find the largest known tetradic prime has paid off with one of 130049 digits: (10^130048)+((9*(10^37077))/11)*(10^46486)+1 This...
In a parallel forum is was accused of "Horrific garbling" - no offense taken by me. What I was trying to say but could not formalise it properly was: Food for...
Suppose that A is a positive integer congruent to 2 or 4 modulo 6 and that N = (2*A^2 + 1)/3 is prime. Conjecture C: (1+x)^((N+1)/4) = A + x/2 mod(x^2-2,N) if...
I now have come to a new conclusion regarding the of order of an element in a group: The following statement is commonly used: If $G$ is a finite group then...
Hi to declare an array, in PARI/GP, simply type the command: arr=[10,20,30,40,50,60,70,80,90,100] By Giovanni  ****************** ****************** ...
The repunits other than 11 are not shown usually as a tetradic prime--Any particular resaon for that. R19,R23.....are all valid candidates...all 1's. ... -- ...
... This is trivial because by definition order(x) = # <x> (cardinality of the *SUB*group generated by x). ... This should better read e_G instead of 1, where...
... I have subsequently shown that all the probable primes with A < 10^10 and the remaining two probable Wagstaff primes, (2^374321+1)/3 and (2^986191+1)/3,...
Best wishes to Norman for the ECPP proof that he is attempting on 2072644824759*2^33333+5 http://anthony.d.forbes.googlepages.com/ktuplets.htm David...
In another place, Anton Vrba mistook himself by claiming that a strong Frobenius test with discriminant 8 proves the primality of probable Wagstaff primes....
Congrats to Andy for http://primes.utm.edu/primes/page.php?id=85646 where the cofactor of N-1 ... entailed a hefty ECPP effort, done by Primo in ... David...
... That sounds much too fast. The certificate in http://www.primes.viner-steward.org/andy/G/5A6F14E3.zip says: [Running Times] Initialization=1mn 43s ...
... In fact, G(p) is not a group but a field ; the multiplicative group of this field has p-1 elements so the story about the order is still (trivially) true. ...
Hi please try the command winpfgw -qr(670781) (form windows, red icon) I get the message: r(670781) is composite: [000000000] (2.282000 seconds) Why? ...
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