Is 1! + 11! + 300! prime?

[Ralf Stephan]

> Is 1! + 11! + 300! prime? It has 602 digits, and the Alpertron calls it
> "unknown" as to primality after half an hour on my Linux box. This is the
> first such case I've encountered in my A! + B! + 1! primality search.

You really should use Pari for this.

? isprime(1+11!+300!)
%1 = 0
? ##
  ***   last result computed in 64 ms.
? factor(1+11!+300!)
%2 = 
[2777 1]

[32957 1]

[267569 1]

[12498091402980688327892288037167822687387567914666313043329685804912534481607780660838705412040185717813161405194124410499366027767026643670475006416813564428875833812689478863818996677458942901183266348828730104068040521670737911684463271494072924048213069623611780557986792028235525897948636423875707805051462603442075440998412521463288071950388929094549311171373698315622239553109019610689044872621607091779786390390669335803529833021549298510568676733317446101586259153146247986530291800114352933085843452770619072390086820741740681502429422872027037209944546624475326934190255974693962232513593261 1]

? ##
  ***   last result computed in 272 ms.

? for(i=1,500,if(isprime(1+11!+i!),print1(i" ")))
17 18 21 42 77 85 
? ##
  ***   last result computed in 1mn, 4,957 ms.

So, no more up to 500.


ralf