Is 1! + 11! + 300! prime?

[Hugo Pfoertner]

Joshua Zucker wrote:

[...]

> So someone
> should still check 693 and 845 ...

PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 693!+11!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
693!+11!+1 is PRP! (69.7657s+0.0193s)
Done.

PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 845!+11!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 29
845!+11!+1 is PRP! (237.4787s+0.0485s)
Done.

The given times are on a 800 Mhz Athlon, running another job. I am
currently preparing tests for the next round of Al Zimmermann's
programming contest, which will be on self-avoiding zigzag paths
("matchstick snakes")

> 
[...]
> 
> For 1! + 17! + n!, my system produced the following candidate primes:
> 11 14 46 183 560

Confirmed with pfgw:
11!+1+17! is 3-PRP! (0.1049s+0.9518s)
14!+1+17! is 3-PRP! (0.0001s+0.0538s)
46!+1+17! is 3-PRP! (0.0003s+0.0415s)
Switching to Exponentiating using Woltman FFT's
183!+1+17! is 3-PRP! (0.9605s+0.9951s)
560!+1+17! is 3-PRP! (30.1122s+6.2870s)

checked:
PFGW Version 1.2.0 for Windows [FFT v23.8]
Primality testing 560!+17!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Running N-1 test using base 23
560!+17!+1 is PRP! (75.0765s+0.0597s)
Done.
Primality testing 183!+17!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Running N-1 test using base 23
Running N-1 test using base 37
183!+17!+1 is PRP! (9.1043s+0.0516s)
Done.
>
[...]
> --Joshua Zucker

To JVP:
Please don't conclude from my contribution that I find this problem very
interesting; I just wanted to confirm Joshua's results.

What I definitely don't support is a series of new sequences:

Numbers n such that n!+k!+1 is prime, for k=1...100.

Hugo Pfoertner