A136295 Multiples of 100 which begin a span of 100 composite numbers.

1671800, 2637800, 3117300, 3933600, 4640600, 4652400, 5178200, 5518700, 5837400, 5845200, 6012900, 6085000, 6333800, 6376200, 6789800, 6958700, 7129900, 7565200, 7803500, 7826900, 8027700, 8367400, 8421300, 8905200

Offset

1,1

Comments

As numbers become large, the proportion of centuries with no primes increases according to the prime number theorem.

References

J. W. L. Glaisher, Factor table for the sixth million : containing the least factor of every number not divisible by 2,3, or 5 between 5,000,000 and 6,000,000; Taylor and Francis, 1883

J. Murray, Report of the Annual Meeting, British Association for the Advancement of Science, Vol. 50 (1881), p. 308.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ n. [Charles R Greathouse IV, Aug 21 2011]

Example

a(2) = 2637800 because there is a prime gap of 112 from 2637799 to 2637911, which makes the century from 2637800 to 2637899 the second one consisting wholly of composite numbers.

Mathematica

100SequencePosition[PrimePi[100Range[90000]], {x_, x_}][[All, 1]] (* Harvey P. Dale, Aug 19 2021 *)

Crossrefs

Cf. A091089, A002386.

Sequence in context: A061127 A183798 A158957 * A250932 A234897 A126437

Adjacent sequences: A136292 A136293 A136294 * A136296 A136297 A136298

Keyword

nonn

Author

Julien Peter Benney (jpbenney(AT)gmail.com), Mar 21 2008

Extensions

Definition clarified by Don Reble, Sep 06 2008

Status

approved