woodhodgson wrote:

> Centuries refer to ranges [100X+1,100X+99]. Does anyone happen to know

> where the first repetition of the primes in a century occurs? I see no reason to

> suspect that this would necessarily happen to be from the first 2 void centuries.

> A very minor point in the prime universe perhaps, but one I have long wondered about.

Assuming you mean two consecutive centuries, the first cases are:

{47326700, 47326800} + {}

{72676000, 72676100} + {33, 57, 69, 81}

{177343900, 177344000} + {9, 39, 93}

{180882800, 180882900} + {17}

{191912800, 191912900} + {}

First case with 0 to 5 primes in the century:

0: {47326700, 47326800} + {}

1: {180882800, 180882900} + {17}

2: {251848800, 251848900} + {1, 43}

3: {177343900, 177344000} + {9, 39, 93}

4: {72676000, 72676100} + {33, 57, 69, 81}

5: {3451361900, 3451362000} + {11, 17, 23, 59, 71}

There is no case with more than 5 below 10^11. There are 5 cases with 5:

{3451361900, 3451362000} + {11, 17, 23, 59, 71}

{34221969900, 34221970000} + {7, 19, 31, 49, 73}

{41290268400, 41290268500} + {1, 7, 19, 31, 73}

{54757509100, 54757509200} + {27, 39, 81, 93, 99}

{94596013600, 94596013700} + {9, 39, 63, 69, 93}

Three consecutive centuries is only possible with no primes since 3

always divides one of {n, n+100, n+200}.

--

Jens Kruse Andersen