A060770 "Early" primes: upper ends of prime gaps that are smaller than the prime number theorem predicts.

3, 5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 47, 61, 71, 73, 83, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283, 311

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• nonn

Examples

			11 is in the sequence because 11/log(11) - 7/log(7) = 0.990... < 1.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Apart from 2 this is the complementary prime set to A060769.

Programs

PARI

{ default(realprecision, 100); n=0; s=2/log(2); forprime (p=3, 12583, if ((r=p/log(p)) - s < 1, write("b060770.txt", n++, " ", p); ); s=r; ) } \\ Harry J. Smith, Jul 11 2009

Formula

A prime p belongs to the sequence iff p/log(p) - q/log(q) < 1 where q is the preceding prime.