A229489 Conjecturally, possible differences between prime(k)^2 and the next prime for some k.

1, 2, 4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 64, 66, 70, 72, 76, 78, 82, 84, 88, 90, 94, 96, 100, 102, 106, 108, 112, 114, 118, 120, 124, 126, 130, 132, 136, 138, 142, 144, 148, 150, 154, 156, 160, 162, 166, 168, 172, 174

Offset: 1

Author

T. D. Noe, Oct 21 2013

Keywords

• nonn

Comments

Are there any missing terms? The first 10^7 primes were examined. All these differences occur for some k < 10^5. Note that the first differences of these terms is 1, 2, or 4.

The similarity to A047233 is understood by a comment in A091666. - R. J. Mathar, Oct 28 2013

Crossrefs

Cf. A000040 (primes), A001248 (primes squared).

Cf. A004277 (conjecturally, possible gaps between adjacent primes).

Cf. A091666 (prime greater than prime(n)^2).

Cf. A229488 (possible differences between prime(k)^2 and the previous prime).

Programs

Mathematica

t = Table[p2 = Prime[k]^2; NextPrime[p2] - p2, {k, 100000}]; Take[Union[t], 60]
NextPrime[#]-#&/@(Prime[Range[100000]]^2)//Union (* Harvey P. Dale, Apr 19 2020 *)