No subject

[N. J. A. Sloane]

 From rkg at cpsc.ucalgary.ca  Fri Sep 22 11:59:21 2000
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Date: Fri, 22 Sep 2000 09:55:57 -0600 (MDT)
From: Richard Guy <rkg at cpsc.ucalgary.ca>
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To: Mario VELUCCHI <velucchi at yahoo.com>
Cc: seqfan at ext.jussieu.fr, njas at research.att.com,
        david.singmaster at vax.sbu.ac.uk
Subject: Re: e(n) = 'Euclid number' = p1*p2*...*pn + 1  >>>>> A SquareFree
 sequences of Numbers?
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Status: RO

It's not your `exact problem' and is not the first reference, but
you might be interested in the following.

When Richard Nowakowski was an undergraduate in a number theory course
he discovered a new(?) proof that there were infinitely many primes
of shape  6n + 1  (actually  12n + 7).  [Recall that Hardy and Wright
only do  4n + 1,  4n + 3  and  6n + 5.]  This resulted in a paper
(after help from John Selfridge & Dick Lehmer):

Richard K. Guy \& Richard J. Nowakowski, Discovering primes with
Euclid, {\it Delta}, {\bf 5}(1975) 49--63; {\it MR} {\bf 52} \# 5548;
{\it Zbl.} {\bf 415}.10008.

There are several similar, but not the same, sequences.
A0945 (M0863) and A09446 (M0864) in EIS are close (dates 1963 & 1984)
but I don't see  2, 3, 7, 31, 211, ...  This is no doubt in the
database, as  njas  has no doubt already pointed out (I haven't read
all my mail yet).     R.

On Fri, 22 Sep 2000, Mario VELUCCHI wrote:

> Dear 'Sequence fans' friends,
> please, do you know the first reference (and follow) for this exact problem:
> 
> -----
>  e(n) = 'Euclid number' = p1*p2*...*pn + 1
> 
>  with: p1 = 2, p2 = 3, ...,pn...:  first 'n' consecutive primes
> 
>  "Are all 'Euclid numbers' of this exact sequence, 'squarefree'?"
> ----
> 
> Thanks for references!
> .marioV
> 
> 
> =====
> Best, Mario Velucchi
> ----- home address ------------------------------- MValg. -
> Mario VELUCCHI  /  Via Emilia, 106  /  I-56121 Pisa - Italy
> ---------------------------------------- Computer & Maths -
> http://www.bigfoot.com/~velucchi
> eMail:velucchi at bigfoot.com
> 
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