woodhodgson wrote:

> While the matter of "centuries" is around again, I have another

> rather idle question regarding centuries that have exactly 10 primes,

> with an even distribution of 1 prime per decade - ie 1 prime in each

> of the following intervals:

>

> [100n+1,100n+9], [100n+11,100n+19], [100n+21,100n+29], ...,

> [100n+91,100n+99].

Up to 10^12 there are 4 cases of more than 17 consecutive decades

with exactly one prime.

The first case has 20 but not in two "centuries":

22497123000+n, for n = 391, 409, 419, 427, 437, 449, 457, 461,

479, 487, 499, 503, 511, 529, 533, 547, 559, 563, 577, 581

The second case has 19:

70739860000+n, for n = 2917, 2929, 2931, 2943, 2959, 2967, 2979, 2989,

2997, 3001, 3013, 3027, 3039, 3049, 3057, 3069, 3079, 3087, 3093

The third case has 22 and includes two consecutive "centuries":

479808685000+n, for n = 481, 493, 501, 513, 529, 537, 549, 553, 567,

579, 583, 597, 607, 613, 621, 637, 649, 651, 667, 673, 687, 691

The fourth case is the first with exactly 18:

806416924000+n, for n = 447, 459, 463, 471, 483, 493, 507,

517, 529, 531, 541, 559, 561, 571, 583, 597, 603, 613

--

Jens Kruse Andersen