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Topic: Sum of primes divided by the next prime
Replies: 6   Last Post: Aug 2, 2006 4:58 PM

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Tapio Hurme

Posts: 853
Registered: 12/8/04
Sum of primes divided by the next prime
Posted: Aug 2, 2006 2:20 PM
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Sum the primes up to p_n. Divide the sum by the next prime p_(n+1):

Sum (2+3+...+p_n)/(p_(n+1))

I found with the aid of excel two examples:

(2+3) = 0 mod 5, i.e. the next prime 5 divides the sum of all the preceding

(2+3+....+61) = 0 mod 67

Below the prime 10009 there is no other cases, except those mentioned above.
Are there any other p_n > 10009 ?


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