Timeline for Are there an infinite number of prime Euclid numbers?
Current License: CC BY-SA 2.5
9 events
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| Nov 12, 2010 at 11:52 | comment | added | François Brunault | According to Ribenboim (The little book of big primes, page 3), it is also not known whether there exist infinitely many composite Euclid numbers. Such questions are often very difficult to tackle. | |
| Nov 11, 2010 at 21:44 | comment | added | Faisal | See also en.wikipedia.org/wiki/Primorial_prime | |
| Nov 11, 2010 at 21:32 | comment | added | Will Jagy | Take a look at $$ $$ arxiv.org/abs/math/0408319 $$ $$ by Granville and Martin. The earlier piece is Rubenstein and Sarnak, Chebyshev's Bias, 1994, for an update see Ford and Sneed, $$ $$ arxiv.org/abs/0908.0093 $$ $$ | |
| Nov 11, 2010 at 21:26 | history | edited | Oleksandr Bondarenko | CC BY-SA 2.5 |
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| Nov 11, 2010 at 21:20 | comment | added | user1073 | Its not a survey article, but your question is discussed in an article of Caldwell and Gallot: ams.org/journals/mcom/2002-71-237/S0025-5718-01-01315-1/… You might try looking at some of their references. | |
| Nov 11, 2010 at 21:18 | comment | added | Will Jagy | You should expect more primes taking your number to be $ 3 \pmod 4$ and $ -1 \pmod q$ whenever you have prime $ q \equiv 3 \pmod 4,$ finally equivalent to your favorite quadratic nonresidue $\pmod p$ for each prime $p \equiv 1 \pmod 4.$ This is by the Chinese Remainder Theorem. Of course there is no attractive formula any more. Some articles have been published on this with part of the title being "primes races," in particular by Peter Sarnak, who may or may not have included the phrase. | |
| Nov 11, 2010 at 21:16 | history | edited | Oleksandr Bondarenko | CC BY-SA 2.5 |
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| Nov 11, 2010 at 21:03 | comment | added | Denis Serre | I don't have the answer. But you may have a look to a related question of mine mathoverflow.net/questions/38794 | |
| Nov 11, 2010 at 21:00 | history | asked | Oleksandr Bondarenko | CC BY-SA 2.5 |