... Did you look at the first link I gave you: http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort It includes those bases searched to 5.074*10^12 (with...
This was meant to be sent to the group and I sent it to Jens by accident. If anyone else here has a PowerPC G5, I have a program that could search a range of...
I did indeed look through all of the interesting links that you sent. I'm just wondering if I can get the time to work through the information and see if it...
Mathematicians studying prime numbers have remarked on the duality of their behavior. For example, Andrew Odlyzko in his 2006 IRMACS lecture, states that "even...
I think the randomness and bell curve are in one sense much more predictable than primes: if you flip a coin long enough, you are eventually going to get N ...
... I suspect it's provable, but I can't locate my copy of Hardy and Wright tonight to skim for inspiration. The minimal value is the column called "order" at ...
The months of April and May have proved very productive with more than 2200 widths with denser packings (some widths with 4 additional primes) The slope of the...
... As always, Tom, thanks for keeping us updated. I'm glad that you're having so much success with such hunts. It's one of the things that I never quite got...
I was having some fun putting (rather arbitrary!) restrictions on the goldbach conjecture to make it come *close* to failing. (Goldbach conjecture: Every even...
Of course if one of your "close" to failing cases is the first of a prime number pair, your next even number will be a close or better success. A real failure...
Mathematics is linked with determinism and predictability. Thus the seeming randomness of primes is striking. The duality is what makes the primes so ...
... Yes. Let d be the smallest value so that p divides b^d-1. First observe that if b^x-1 and b^y-1 and both divisible by p^2 (or any other number), then...
I was reading where if Merten's sum of Moebius terms could be shown to be big O of k^(1/2+epsilon) that it proves the Riemman hypothesis. I was looking at the...
I was doing some thinking the other day, and ran into some neat stuff: What percentage of all integers are even, or divisible by 2? At first, I thought it...
... Research "Natural Density". The limsup and liminf converge to 50%, so it's 50%. Quite why you don't think the density on the sets {0,1} and {0,1,2,3}, ......
Thanks! Much appreciated, really interesting stuff. ... Boardwalk for $500? In 2007? Ha! Play Monopoly Here and Now (it's updated for today's economy) at...
... I'm not sure what you mean by "solely divisible by that number alone". Phil guessed you meant least prime factor (lpf). I also guess that, but then your...
Ahh, good catch. Yeah, my numbers were off... I'm kind of interested in what the graphs look like, because I've never encountered another series of numbers...
... primes.) ... It turns out that for GP Pari to work on my mac, I needed to get a C compiler which will produce programs which could run on the mac. Apple ...
Actually, I was wondering if there was a way to predict the lines without knowing the primes in question... an approximation, at the very least. I was thinking...
... You'll probably note, if you follow the discussions in this group, that a large number of participants use the free PARI/GP package for number theory...
Sorry, Forget that, I hadn't checked for divisibility by 1896 before I posted. Which is what comes of too much haste and not enough speed. Kevin. ... I'm...
Hello, I have found in few seconds with my program: 2^1896 have prime factor 201487636602438195784363 I don't know, this factor are known ? regards ...
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