A071572 Least k such that nextprime(k*prime(n)) - k*prime(n) is nonprime.

1, 2, 2, 1, 2, 1, 5, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1

Offset: 1

Author

David W. Wilson and Robert G. Wilson v, May 31 2002

Keywords

• nonn

Comments

The first time a value of m appears is when n equals 1, 2, 20, 45, 7. I can find no value greater than 5 for n's up through 12,500,000.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{k = 1}, While[ PrimeQ[ NextPrim[k*Prime[n]] - k*Prime[n]], k++ ]; k]; Table[ f[n], {n, 1, 105}]