Small mistake on my part too, I'm afraid (one really shouldn't initialize an email using CTRL-C+CTRL-V...):- For "APSieve" read "NewPGen". Thanks for updating...
... Congrats on those! I would be really interested in some details and run-times of your algorithm for finding APn's. Your methods are obviously very...
... Smallest known difference and end for an AP23. ... Not a record after the former AP23 is known. ... This is the largest known AP22 from March 15: ...
... The equation (i^3 + k*(i^2+1))^2 + 1 = 0 shows that there is a loop for every GFN seed. For example http://primes.utm.edu/primes/page.php?id=21515 helps ...
... Thanks. ... All my largest known AP records are on the form a*p#+1 for an AP of a's. I haven't searched AP lengths above 19 with this program. For AP sizes...
... Thanks for that description, Jens. Apart from the first and last of these features, that is precisely my detector too (it's exhaustive, but doesn't try to...
http://primes.utm.edu/primes/page.php?id=77458 ... Perhaps Mike needs to submit the other 5, even though those supporting primes are unlistable? David...
... If it's exhaustive then it may spend time testing different parts of the same potential AP of target length. No cache optimization is bad in a program...
... The beauty of working in terms of APs which straddle a particular point (the half-way index) is that this can be avoided. I start only from an AP2 which...
Conjecture: An odd prime p is a generalized Fermat prime if and only if there exists an integer i with i^2 = - 1 mod p and i^2 < p. Small number check: ...
... Andrey: You simply /restated/ my conjecture. What I want is the proof! Why cannot there be an integer i=sqrt(Mod(-1,p)) with i^2 < p-1 ? There is none for...
... But if i^2 = p-1, then p = i^2+1, i.e. obviously a GFP... ... But if 0 < i^2 < p-1, how i^2 could be -1 mod p? Andrey [Non-text portions of this message...
Andrey sagely observed that ... Maybe, before I go to sleep, I should give the context. In http://groups.yahoo.com/group/primeform/message/7179 the GFN-helper ...
... Jens: if you don't mind, can I probe a bit here? The question is important, if we are to home in on the optimal coding. I have stored all the candidate k...
Hi, I have found an interesting function which I call pipips(n) . It is the count of prime-index-primes (pips) less than n. We define pip(n) = prime(prime(n))...
... to which one may quickly add pi(pi(10^14)=115465507935 [R(R(10^14)]=115465491695 pi(pi(10^15)=995112599484 [R(R(10^15)]=995112567449 But why confine the...
... Yes, table=array. ... I have limited knowledge of how cache actually works. If MB's of other data has been read from ram since the next value of q was last...
The first 47577 digits of the decimal expansion of Pi (counting 3 as the first digit) give a (probable) prime. This extends the sequence of known (probable)...
... But Eric, it's not prime trivia, since the number has not been proven prime :-) I think that it might also be welcomed at http://primes.utm.edu/curios/ ...
... Here is a construction that will tune log(i)/log(p) to any fraction in the range (1/2,2/3). Suppose that n is completely factorized and that p = (n*b+1)^2...
My algorithm is several orders of magnitude faster then what you guys have/propose, and the more primes you throw at it the faster it gets. In the simplest...
Jens, The Athlon XP's, to my experience have two flavors: 256kb and 512kb of L2 cache. I suspect the later (final run) of XP's were pushing 1mb of L2. The...
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