Timeline for Can $b^4+1$ be a pseudoprime to base 2 (except for Fermat numbers)?
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8 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Mar 29, 2016 at 21:30 | vote | accept | Jeppe Stig Nielsen | ||
| Mar 26, 2016 at 20:30 | comment | added | Jeppe Stig Nielsen | @JeremyRouse Somewhat interestingly, the $46657$ you mention is also the first pseudoprime we find with $b^2+1$ which means of course that we have a sixth power whose successor $n=6^6+1$ is a pseudoprime. If we disregard again Fermat numbers A000215, this appears to be the only case $n=b^a+1$ with exponent $a\ge 4$ one finds "immediately". | |
| Mar 24, 2016 at 14:38 | answer | added | Stefan Kohl♦ | timeline score: 10 | |
| Mar 24, 2016 at 0:32 | comment | added | Jeppe Stig Nielsen | @JeremyRouse Yes, that is cool! Originally, I was mostly motivated by finding actual primes and how often a "probable prime" to base 2 would come out composite, and maybe for that reason I had not really considered $b^3+1=(b+1)(b^2-b+1)$. Now I am about to submit $12, 36, 138, 270, 546, 4800, \ldots$ to Sloane's OEIS. | |
| Mar 23, 2016 at 17:54 | comment | added | Jeremy Rouse | For comparison, there are many base 2 pseudoprimes of the form $n = b^3 + 1$, including $n = 1729$ and $n = 46657$. | |
| Mar 23, 2016 at 15:51 | review | First posts | |||
| Mar 23, 2016 at 16:06 | |||||
| Mar 23, 2016 at 15:49 | history | asked | Jeppe Stig Nielsen | CC BY-SA 3.0 |