

A136295


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


1



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



FORMULA



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



KEYWORD

nonn


AUTHOR

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


EXTENSIONS

Definition clarified by Don Reble, Sep 06 2008


STATUS

approved



