8

In Wikipedia , Miller-Rabin-Test, it is mentioned that the smallest strong-Fermat pseudoprime to the prime-bases upto $41$ is $$3,317,044,064,679,887,385,961,981$$

Hence, every number smaller than this number is prime, if it passes the Rabin-Miller-test for the prime-bases upto $41$.

Has this result been doublechecked ?

How long would such a doublecheck take ? Is there a method more efficient the enumerating all numbers upto that point ?

Community
  • 1
Peter
  • 86,576
  • Reference 13 in that article seems to provide the results. You're looking for another? – John Aug 24 '18 at 14:10
  • 1
    @John This was one calculation, right ? I am looking for a doublecheck , that means a calculation independent from the one you mentioned. Unless, your reference is already a repitition of the calculation. – Peter Aug 24 '18 at 14:24
  • 1
    So the answer is yes. :) – John Aug 24 '18 at 16:25
  • 1
    @John It's Wikipedia, so Peter is right to be extremely skeptical. It's very easy to invent plausible-sounding citations on Wikipedia. – Robert Soupe Aug 25 '18 at 03:23
  • 1
    @RobertSoupe Such important results should always be doublechecked (no matter what the source is). Since apparently, no shortcut is known, the high limit (about $3\cdot 10^{24}$) legitimates at least doubts. Unfortunately, this is also true for other extremely time-consuming calculations, for example, do we actually know that there is no third Wieferich prime below , lets say $10^{15}$. I am not ultrasceptical, but I also do not believe everything that is posted on some popular site. – Peter Aug 25 '18 at 11:03
  • Indeed. I started to read the referenced ArXiV paper. But way too many people don't even bother to at least click on citation links. – Robert Soupe Aug 26 '18 at 02:54

1 Answers1

1

The primary and AFAIK only peer-reviewed reference is: Jonathan Sorenson and Jonathan Webster, Strong pseudoprimes to twelve prime bases, in Mathematics of Computation 86 (2017), 985-1003.

OEIS A014233 has other relevant references and fact.

Here is the section of the Wikipedia article discussing that.

fgrieu
  • 1,828