In response to a problem posed by Zak Seidov on the "Prime Numbers" Yahoo!Group.
Here's a table of the smallest primes a(n) such that the sum of primes 2..a(n) ends with a consecutive run of n 0s :
| n | a(n) | sum | #primes | discoverer |
|---|---|---|---|---|
| 1 | 5 | 10 | 3 | Zak Seidov (all verified) |
| 2 | 23 | 100 | 9 | |
| 3 | 35677 | 63731000 | 3795 | |
| 4 | 106853 | 515530000 | 10183 | |
| 5 | 632501 | 15570900000 | 51531 | |
| 6 | 31190879 | 29057028000000 | 1926965 | |
| 7 | 58369153 | 98078160000000 | 3471031 | |
| 8 | 707712517 | 12606879200000000 | 36631619 | |
| 9 | 26219976521 | 14640561651000000000 | 1142888527 | Phil Carmody (unverified) |
| 10 | 87424229843 | 154819819890000000000 | 3620253377 | |
| 11 | 1642257355619 | 48827520934500000000000 | 60628893281 | |
| 12 | ??? | ? | ? | (your name here?) |
I'd expect these to grow slightly faster than exponentially.
Number of primes for the 9,10 and 11 terms were found using The Nth Prime Page. (It was easier than keeping a tally as I went.)
For those that trust my figures and wish to look further (don't do this, verify my results first please), I think that the sum of the primes from 2 to 2366226636001 is 100043148001098034737721
Last modified 2003/07/22
Another hastily constructed page by Phil Carmody
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