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• ... 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,
Message 1 of 37 , Jul 19, 2011
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
• ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens Kruse Andersen
Message 37 of 37 , Dec 31, 2012
Jaroslaw Wroblewski wrote:
> Here is 5th known large prime 19-tuplet:
>
> 2406179998282157386567481191 + d,
> d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
> (28 digits, Dec 2012, Raanan Chermoni & Jaroslaw Wroblewski)
>
> This sets new records for 18 and 19 Simultaneous Primes.

Congratulations!
http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated.

--
Jens Kruse Andersen
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