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

Author

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

Keywords

• nonn

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A091089, A002386.

Programs

Mathematica

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

Formula

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

Extensions

Definition clarified by Don Reble, Sep 06 2008