A378429 Numbers k such that the prime gap between the consecutive primes p1 < k# = primorial(k) < p2 sets a new record.

3, 7, 13, 17, 23, 29, 37, 43, 47, 61, 71, 79, 83, 97, 101, 109, 137, 193, 347, 349, 409, 457, 587, 599, 887, 929, 967, 1319, 1801, 1877, 2081, 2687, 2731, 2741, 2843, 2939, 2957, 3673, 3823, 4621, 5717, 6011, 6151, 6563, 6863, 7393, 8389, 9833, 11903, 12547

Offset: 1

Author

Jean-Marc Rebert, Dec 20 2024

Keywords

• nonn

Examples

			a(1) = 3, because the prime gap between the consecutive primes 5 < 3# < 7 sets the first record of 2.
 n gap       p1        a(n)#        p2
 1   2             5 <   3# <             7
 2  12           199 <   7# <           211
 3  18         30029 <  13# <         30047
 4  48        510481 <  17# <        510529
 5  80     223092827 <  23# <     223092907
 6 102    6469693189 <  29# <    6469693291
 7 120 7420738134751 <  37# < 7420738134871
		

Crossrefs

Cf. A001223, A058044, A034386, A350100.

Extensions

a(32)-a(39) from Amiram Eldar, Dec 20 2024

a(40)-a(50) from Michael S. Branicky, Dec 21 2024