primality test please?

[Joshua Zucker]

I wrote a short program to extend A078154 but I only have a
probably-prime test readily available (a bunch of Miller-Rabin
iterations).  Could someone with the software handy please check
whether the following numbers are really prime? (I'm pretty sure 2 3 7
13 and 73 are :)

My search up to 500! didn't find any more than these -- but I think
this is enough for OEIS!

The corresponding values of n (for n!, strip trailing zeros, and add
1) are 1, 2, 3, 5, 6, 14, 15, 24, 74, 191, 222, 276.

By the way, if whoever checks the primality of these wants to submit
the extension, that's fine with me.  I've just decided it would be fun
to see how many "more" sequences I can take care of this afternoon --
some of them are pretty easy to compute!  (But most of the
easy-to-compute ones are not very interesting.  I'd like to have a
world where only interesting sequences come up in OEIS when you look
at those that want more terms.)

Thanks,
--Joshua Zucker

2
3
7
13
73
871782913
1307674369
62044840173323943937
33078854415193864122595302822125378214568325182093497117061192683541123570097156545925087233
184894163097375258881955918429152826023486880074840881190341424470932398307421858765932989891230617236011433086046446873698686502383887246269538075751243803690165077660545947879780035070755325602291210586363266685747215397109200906567725889375959407956822043265112098990118206440233050664892657426489533267969
11205075580064413918282465787428850331618234483620107256641806644257517065448960498845547308589123315272225515821582083550911856777042555566494995461508350030412945015928362037889500879028802533114006644956482648450865757931592560691748095501378019639237014185141846525204926394414526091187114744532820374516851036885491563728009958826486619432294797566054909576516569399297
27880801049576391916809030013144803653582088085945797282932848129210967673212370149756485598094028320802167208456352104968801418454959364173553213514951992303017183103403646074562514526295519450915694443621174002472447545100808157100394086420044133132593127314754419902210759757720908701681929575698213583840575725184603324241231125460092185394583504987959144851257371160135965934520932367028741342341978309460617633241187617316354149500629794151541639424991935676497280957002403033382913