Near Integers

[N. J. A. Sloane]

so maybe it wasn't a good idea to post that message to the whole list.
so that the descriptions will become:
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Subject: 37
From: Artur <grafix at csl.pl>
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I was look for such prime numbers p that Sum 1/i^3 from 1 to p-1 is  
divisable by p^3
After 49 hours of working my computer answer was that only one such prime  
is 37 and no more up to 1000000
Any comment ?
ARTUR