A217724 Smallest prime producing a gap with the next prime, the size of the gap being a composite number with 2n+1 as a factor.

139, 1831, 1129, 2971, 1327, 19333, 81463, 19609, 44293, 89689, 173359, 212701, 265621, 544279, 1100977, 396733, 1098847, 370261, 1349533, 6752623, 5518687, 6371401, 10343761, 2010733, 4652353, 33803689, 83751121, 38394127, 39389989, 79167733, 142414669

Offset: 1

Author

Robert Price, Mar 21 2013

Keywords

• nonn

Comments

The "gap" is defined as the number of integers between two primes. If the two primes are p1 and p2, then the size of the gap is p2-p1-1.

For at least n<=100, the gap is minimal and is 3*(2n+1).

Examples

			For n=2, the required gap is a composite number with 5 (2n+1) as a factor.  The size of all gaps are odd, so gaps of 15, 25, 35, etc. are required.  The prime 1831 and its next prime of 1847 produces a gap of 15.  1831 is the smallest prime with this property.
		

Links

• Robert Price, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A067836.