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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'twin prime conjecture'
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Generalization by Larry Hammick
Correction id: 1459
Filed on: 2003-01-10 00:38:13
Status: Rejected on 2003-01-26 09:42:14
Type: Addendum
Correction text:
| Here's a bit I would add. Let a_1 ... a_n be integers such that for any modulus m>1, there is some n in [0,m-1] such that none of the a_i is congruent to n mod m. (In other words, the a_i don't "cover" the residue classes mod m, for any m>1.) Then (conjecture) there are infinitely many x such that x+a_i is a prime for all i. The twin primes conj. is the special case a_1 = 0 and a_2 = 2. I don't have the formula handy, but there is a conj. about the approximate number of such x up to a given limit. That number is what one would expect if (as is expected) the count of primes up to x is x/(log x) + [some error term], but the distribution of primes is "otherwise random". |
No comment from correction handler vmoraru.
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