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OEIS A014545 says 1+13494## is a prime number but factordb.com says it is composite, where n## is the product of first n primes on factordb. Which is correct?

edit: Sorry if my question is not appropriate here. I found some small prime numbers of the form 1+n##, and looked them up in OEIS to find this number. Then I also looked it up in factordb and found that it says not a prime. I wondered if there was a mistake in the OEIS or factordb, so I asked this question. I want to know whether factordb or OEIS is correct.

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    $\begingroup$ Have you performed a Rabin-Miller primality test? $\endgroup$
    – supinf
    Dec 14, 2020 at 10:48
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    $\begingroup$ Please read how to ask a good question, and in particular do explain why you are interested in this number. $\endgroup$
    – user21820
    Dec 14, 2020 at 12:30
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    $\begingroup$ @user21820 I disagree. The question is both interesting and motivated It is clearly explained why the author is interested in this particular number. $\endgroup$
    – Peter
    Dec 14, 2020 at 12:46
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    $\begingroup$ If I remember right, factordb had some problems with "##". This could explain the error. $\endgroup$
    – Peter
    Dec 14, 2020 at 12:53
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    $\begingroup$ @user21820 Maybe this is the first discrepancy that hgut found? Certainly this is the first that I recall. I think the relevance of this question is justified. $\endgroup$
    – supinf
    Dec 14, 2020 at 13:49

1 Answer 1

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Accoridng to PFGW, the number is $3$-PRP. This does not prove the primality but chances stand very good.

PFGW Version 4.0.1.64BIT.20191203.Win_Dev [GWNUM 29.8]

145823#+1 is 3-PRP! (120.3835s+0.0233s)

Done.

This number can be proven prime with the p-1-method. Perhaps someone does this.

UPDATE : The number passed a miller rabin test with $5$ random bases.

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  • $\begingroup$ what does 3-PRP mean? $\endgroup$
    – supinf
    Dec 14, 2020 at 12:56
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    $\begingroup$ It passes the weak Fermat test with base $3$ $\endgroup$
    – Peter
    Dec 14, 2020 at 12:56
  • $\begingroup$ Isn't it possible to perform the p-1 method with PFGW? $\endgroup$
    – user854931
    Dec 15, 2020 at 0:21
  • $\begingroup$ I know I'm late to point this out, but the Question involves the twice primorial $1+13494##$, not $1+145823#$. But your Comment on the Question shows you were aware of the double primorial aspect. $\endgroup$
    – hardmath
    Mar 15, 2023 at 0:57

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