This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
6! - (6-1)! + 1 = 601 is prime.
Do[ If[ PrimeQ[n(n +1)!/2 +1], Print@ n], {n, 4000}] (* Robert G. Wilson v, Apr 05 2018 *)
isok(k) = ispseudoprime((k+1)! * k / 2 + 1);
select(p -> isprime(p) and isprime(p*factorial(p) + 1), [$2 .. 200]);
Select[Range[2, 200], PrimeQ[#] && PrimeQ[#*#! + 1] &] Select[Prime[Range[100]],PrimeQ[#*#!+1]&] (* Harvey P. Dale, Mar 21 2025 *)
a = List(); for(p=2, 200, if(isprime(p) && isprime(p*p!+1), listput(a, p))); a
[p for p in range(2, 200) if is_prime(p) and is_prime(p*factorial(p) + 1)]
select(p -> isprime(p) and isprime(p*factorial(p) - 1), [$2 .. 600])
Select[Range[2, 600], PrimeQ[#] && PrimeQ[#*#! - 1] &] Select[Prime[Range[110]],PrimeQ[# #!-1]&] (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Feb 12 2025 *)
a = List(); for(p=2, 600, if(isprime(p) && isprime(p*p!-1), listput(a, p))); a
[p for p in range(2, 600) if is_prime(p) and is_prime(p*factorial(p) - 1)]
The initial terms, in decimal and in factorial base, are: n a(n) fact(a(n)) - ------- ----------------- 0 2 1,0 1 2 1,0 2 5 2,1 3 19 3,0,1 4 97 4,0,0,1 5 601 5,0,0,0,1 6 4327 6,0,0,1,0,1 7 35281 7,0,0,0,0,0,1 8 322571 8,0,0,0,0,1,2,1 9 3265949 9,0,0,0,0,1,0,2,1
a(n) = { forprime (p = n*n!, oo, my (q = p); for (r = 2, oo, if (q==0, break, q % r==n, return (p), q \= r););); }
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