A219789 Least prime in the form x*y-1 with x > 0, y > 0 and x + y = n > 3.

2, 3, 7, 5, 11, 7, 23, 17, 19, 11, 23, 13, 47, 29, 31, 17, 83, 19, 71, 41, 43, 23, 47, 71, 131, 53, 103, 29, 59, 31, 167, 149, 67, 101, 71, 37, 383, 113, 79, 41, 83, 43, 167, 89, 251, 47, 263, 97, 191, 101, 103, 53, 107, 109, 311, 113, 223, 59, 431, 61, 239, 353

Offset: 4

Author

Zhi-Wei Sun, Nov 28 2012

Keywords

• nonn

Comments

See comments in A091182, A219782 and A219791.

Examples

			a(6)=7 since 6=2+4 with 2*4-1=7 prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 4..10000
• Zhi-Wei Sun, An amazing conjecture on primes, a message to Number Theory List, Nov. 27, 2012.
• Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588.

Crossrefs

Cf. A091182, A219782, A219791.

Programs

Mathematica

Do[Do[If[PrimeQ[k(n-k)-1]==True, Print[n," ",k(n-k)-1]; Goto[aa]], {k,1,n/2}]; Print[n," ",counterexample]; Label[aa]; Continue, {n,4,100}]
Table[k = 1; While[p = k*(n - k) - 1; k <= n/2 && ! PrimeQ[p], k++]; If[k > n/2, Print["counterexample at n=", n]; p = 0]; p, {n, 4, 100}] (* T. D. Noe, Nov 28 2012 *)