Hi All,

Long long ago 19 Dec 2002 (post 10359) Sebastián Martín Ruiz asked

Let F(n)=P(n)!-P(n)!!+2

P(n) n-th prime

F(1)=2 Prime

F(2)=5 Prime

F(3)=107 Prime

F(4)=4937 Prime

Find another prime number in this secuence

to which I replied (without proof as I could only show that it was

Fermat and Lucas PRP)

(1667!)-(1667!2)+2

However as it has 4650 digits I thought it should be provable.

David Broadhurst pointed me to Marcel Martin's Primo (a marvellous

program).

I started primo 2.0.0 on 1667!-1667!2+2 and left it for what I

thought

would be 6-12 months.

It has finished after "only" 1340h 11mn 39s

the result being

[PRIMO - Task Report]

Version=2.0.0 - beta 3

Task=Certification

ID=B285E020B5C1A

Created=01/15/2003 09:31:38 AM

[Common]

Path=C:\Program Files\Primo200\f1667\

Selected=1

Processed=1

Certified=0

Candidate #1=Failed, 1340h 11mn 39s

[Candidate #1]

Input=Primo-B284302D531FB-001.tmp

Output=Primo-B284302D531FB-001.tmp

Status=Failed, impossible to certify current N

Not! what I was hoping for.

Changes to Primo made it worthwhile trying again

This time Primo sucessfully proved 1667!-1667!2+2 Prime

[PRIMO - Primality Certificate]

Version=2.2.0 beta 3

WebSite=

http://www.ellipsa.net/
Format=3

ID=B2A0002ACB343

Created=03/08/2004 12:29:39 PM

TestCount=614

Status=Candidate certified prime

[Running Times]

Initialization=1mn 46s

1stPhase=2071h 22mn 47s

2ndPhase=563h 45mn 34s

Total=2635h 10mn 8s

[Candidate]

File=D:\Primo220\wrk\f1667\f1667.in

Expression=1667!-1667@2+2

Cheers

Ken