More than a year ago there were some messages about "Proth weight" and "Nash
weight", i.e. the weight of k for k*2^n+1 and k*2^n-1 respectively. As for twin
pair, the weight of k, I think, will not be the multiply of "+1" and "-1"
k-weights. Generally, given n, the behaviour of first odd k's for which
k*2^n+/-1 are twins is quite interesting. Sometimes first such k is extremely
large or small, independently of the weight of k or n.
Have anybody studied these things? Maybe Daniel Papp (g259) knows some
tricks?..
Here's the list of first odd k's for which k*2^n+/-1 are twins, n from 1 to
1000 (the most of terms was quickly generated by APSieve, thanks to Michael Bell
et.al.):
This sequence of k's is already interesting (e.g., 125385 appears 2 times,
27261 - 3 times), but the sequence of k/n^2*twinweight(n) would be yet more
informative.
Thanks for comments,
Andrey
[Non-text portions of this message have been removed]
Hello! More than a year ago there were some messages about "Proth weight" and "Nash weight", i.e. the weight of k for k*2^n+1 and k*2^n-1 respectively. As for...
... [SNIP] ... Your observation is correct. The reasons why the ks have various Proth/Nash weights is because various subsets of ns are forbidden from being...
... 'PSieve', a program that Chris Nash and I worked on quite a while ago, enabled the weights of many things to be investigated, including twins. In fact, at ...
Can anybody find a value of k which yields more twin primes than k=202507305 (3*5*7*11*13*13487) ? When k=202507305, k*2^n+/-1 are twin primes for n: 2, 12,...
... Jack This goes to show it sometimes takes a while to reply to posts, in this case 2 1/2 years! In any case the following k has 13 twins to n=10000 ...
... That's a pretty good one, and the last 5 of those exponents... wow! I would have expected my "record" to be beaten by a k value with an abundance of small...
... in ... wow! I know, extraordinary to get 5 after n=484 ... I agree, but they are not so easy to find - 10 twins to n=100 is not too hard, but getting those...
... See also my announcement on NMBRTHRY a couple of years back. I believe I injected the 15-twin k into a usenet post at about the same time, if you really...
... Yes, 5*2^n-1 and 5*2^n+1 are never both prime. :-) The same is true of all k>3 which are not divisible by 3. The interesting value of k is k=111, which is...
... I should clarify that when extending the Sierpinski problem to twin primes, we must impose the additional requirement that k be divisible by 3 -- without...
... Elizabeth Regina I might have protested at that "must", but I bow to the good humour of ... But my word, your non-trivial case ABC2 111*2^(36*$a-25)+1 |...
... Doing the same with k=1341 (where n must be equal to 21 mod 36): ABC2 1341*2^(36*$a-15)+1 | 1341*2^(36*$a-15)-1 a: from 1 to 200 1341*2^(36*14-15)+1 ...
Has anybody thought of taking this problem sideways in a dual Sierpinski problem manner? i.e. is there a k such that 2^n+k and 2^n+k+2 (or 2^n+k-2 if you want...
... Surely the dual would be k such that 2^n+k and 2^n-k are never prime? Paul. __________________________________________________ Virus checked by MessageLabs...
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