Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: 19 + 13234551541698967679 * 17# * n, n=0,...,18 (27 digits) At the moment it is...
Can anyone know or find 3 (or more) consecutive primes with common gap 300? Just from curiosity, thanks [Non-text portions of this message have been removed]...
A prime P which turns into a composite if you alter any bit in its binary representation is an "every bit matters" prime. The examples below 10000 are 127,...
Find a rational point on the curve y^2 = x^3 - 6077 Hint: there is exactly one. Comment: the rationale for posting to this list is that prime numbers play a...
... Ok. You mean use a complex number as base instead of using a positive number as base. ... Ok. You mean that your exponents will be general positive...
A beautiful day, a very brief proposition for a better factorisation algorithm, based on the basic ideas of Pollard p-1 algorithm 1. Instead of using N, take C...
I asked about any proof for my conjecture in Math.StackExchange<http://math.stackexchange.com/questions/318412/proof-of-prime-maker-conjecture>a month ago with...
After 617 days of up time, the computer center is shutting down and moving the primes.utm.edu web server. Should all go well, it should only take 15 minutes...
Recently we had a great discussion during a meeting with colleague matematicians and we opened a theme that seems to get quite an interesting intellectual...
A[0]=0 A[1]=1 A[n] = 3*a[n]-a[n-1]+2 this begins 0, 1, 5, 16, 45, 121, 320 and there is a page on it here: http://oeis.org/A004146 The parities repeat...
The wiki page on Formula for primes, says: In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No...
I succeeded in programming such a test. It is a combination of a base-2 strong pseudoprime test and a certain Lehmer test. No multiprecision math libraries...
Hi, perhaps the gremlins will like this puzzling composite test. For non-square n coprime to 30 find x and a: kronecker(x^2-4,n)==-1 gcd(x^3-x,n)==1 ...
1: If k is a positive integer such that there does not exist a nonzero m, different than k, such that (6 m + 1) divides (k-m), then (6k+1) is prime. 2: If k is...
http://www.newscientist.com/article/dn23171-largest-fake-prime-number-holds-300-billion-digits.html Does anybody volunteer to run BPSW on this number?...
//Code by Warren D. Smith, March 2013. Compiles with gcc. //Speed, on 2GHz intel gcc 4.2.1, is about 25 minutes to test 2^30 consecutive integers... //i.e....
Hi, first post, I have developed a formula for checking divisibility of numbers but need verification before I start using computers to test speed of the...
It is notable that http://physics.open.ac.uk/~dbroadhu/cert/gigantic.txt now contains 5 proofs of primality above 50k digits for which great effort was...
If you are programming a new sieve, I'd rather like it if you tried this so you could do something new. Naive Eratosthenes: runtime=NloglogN word-ops memory=N...
Hi, I have a question where I need a very very reliable answer: Does there exist any function in the world to which I can input the first 6 prime numbers and...
Hi, Forgive the intrusion as I'm a physicist with an interest in efficient computing rather than a mathematician who has studied number theory. In order to...
I have been working on some compression notions regarding primes. If anybody has references on what's out there already on this matter, if what I am doing is...
After a few restless nights, thinking about prime numbers, it finally dawned on me. . . Heuristically, every natural number, N, greater than 3, contains at...
Below are new record 17 & 18 prime tuplets (and new 17 & 18 Simultaneous Primes records): Prime 18-tuplet 601884606346328759496455407 + d, d = 0, 4, 10, 12,...
Since you asked... If F(n) is the nth Fermat prime, then sum(n odd) 1/F(n) and sum(n even) 1/F(n) and product(n odd) (1-1/F(n)) and product(n even) (1-1/F(n)) ...
... Thank you David. I see how (zeta(2))^2/zeta(4) = (p^2+1)/(p^2-1), but how do we know what zeta(2) is, and how do we know what zeta(4) is? zeta(2) = sum(k...
hi C_twin=pi^2/12*prod(p>=5 odd primes) (1-2/(p*(p-1)))=0.66016.. You will need tens of thousands of terms to get several decimal places, but the appearance of...
