A299791 2-provable primes: Primes p expressible as x+y, where the prime factors of x and y are precisely the primes less than sqrt(p).

5, 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 167

Offset

1,1

Comments

There cannot be any terms > 169 because the least possible value for x+y once 13 is included in the set of prime factors is 347 > 17^2. For p > 347, the list of factors required in x or y also includes 17, pushing the minimal p to 1429 (714 + 715). This in turn adds the next 5 primes to the list, pushing the minimal value of x+y exponentially upward relative to p.

Links

Table of n, a(n) for n=1..32.

Example

The primes less than sqrt(167) are 2, 3, 5, 7, and 11, and 167 = 2*3*3*5 + 7*11, so 167 is in this sequence.

Crossrefs

Sequence in context: A288445 A087759 A234644 * A230359 A161548 A090320

Adjacent sequences: A299788 A299789 A299790 * A299792 A299793 A299794

Keyword

nonn,fini,full

Author

Charlie Neder, Jan 21 2019

Status

approved