

A060769


"Overdue" primes: upper ends of prime gaps that are larger than the prime number theorem predicts.


4



29, 37, 53, 59, 67, 79, 89, 97, 127, 149, 191, 211, 223, 251, 293, 307, 331, 347, 367, 397, 409, 419, 431, 457, 479, 487, 499, 521, 541, 557, 587, 631, 641, 673, 691, 701, 709, 719, 727, 751, 769
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OFFSET

1,1


LINKS



FORMULA

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


EXAMPLE

79 is in the sequence because 79/log(79)  73/log(73) = 1.065... > 1.


PROG

(PARI) { default(realprecision, 100); n=0; s=2/log(2); forprime (p=3, 26203, if ((r=p/log(p))  s > 1, write("b060769.txt", n++, " ", p); ); s=r; ) } \\ Harry J. Smith, Jul 11 2009


CROSSREFS

Apart from 2 this is the complementary prime set to A060770.


KEYWORD

nonn


AUTHOR

Ulrich Schimke (ulrschimke(AT)aol.com)


STATUS

approved



