Timeline for answer to Arithmetic progressions, given a prime by Gerry Myerson
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| May 23, 2020 at 12:38 | comment | added | user137748 | My original question asks only for one A.P. in primes, whose first term is $p$ (and in particular, $3$), but a natural extension would be to ask what you have stated- if there are infinitely many such 3-A.P.s, given a prime $p$. Of course, the Dickson's conjecture is far more general than that. Also, that is a neat reformulation in the first sentence- one is, after all, only really checking 'prime-ness' for the third term, since every prime greater than $3$ forms a 2-A.P. with $3$. Thanks! | |
| May 23, 2020 at 12:36 | comment | added | Stanley Yao Xiao♦ | It is very rare to have a result in prime number theory that produces an example of something without proving that there are infinitely many. The reason is because almost all (and as far as I know, ‘almost’ can be dropped) methods that produce primes actually produces an asymptotic lower bound (or asymptotic formula) for how many such primes there are up to some height. So in practice, the question you asked and the question Gerry Myerson answered are equivalent. | |
| May 23, 2020 at 6:47 | history | answered | Gerry Myerson | CC BY-SA 4.0 |