# Superduperfactorial Primes: Primes of the form A055462(k)-1 or A055462(k)+1.

Jonathan Post jvospost3 at gmail.com
Sun Sep 2 18:49:51 CEST 2007

```Thank you, Maximilian.  I cited you in this submission to the Prime
Curios page, where  I rank #5 with 205 listings.

To: editor
Subject: New Prime Curio about 5944066965503999 by Post
From: Prime Curios! automailer for <jvospost2 at yahoo.com>

There has been a new curio submitted for your approval:

5944066965503999 [number_id=7238]

The largest known superduperfactorial prime, those being
primes of the form (product of first n superfactorials)
plus or minus 1. The superduperfactorial primes known as of
1 Sep 2007 are 2, 3, 23, 6911, 238878721, 5944066965503999.
For example, 6911 = (1!2!3!4!)(1!2!3!)(1!2!)(1!) - 1 =
288*12*2*1 - 1 = 6912-1. As Maximilian Hasler replied to me
when I emailed these first 6 values, after he programmed in
PARI and searched, there is no other prime of the form
A055462(k)-1 or A055462(k)+1 for k < 30, for which
A055462(30) ~ 10^3849.

Reference: A055462 Superduperfactorials: product of first n superfactorials.
[Post]

On 9/2/07, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
> That's easily PARI-ized:
>
> A055462(n)=prod(i=2,n,i^((n-i+1)*(n-i+2)/2))
> for(i=1,30,if(isprime(t=A055462(i)-1),print1(t",
> "));if(isprime(t=A055462(i)+1),print1(t", ")))
>
> but except 2,3,23,6911,238878721,5944066965503999
> there is no other prime of that form for k < 30, for which
> A055462(30) ~ 10^3849, so the next
> term would be anyway to large to include in OEIS.
>
> Maximilian

```

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