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#1 2013-02-23 11:42:32

mblacob1947
Member
Registered: 2013-02-23
Posts: 1

Prime numbers

Is is known that:

The formula (a+1)**n - a**n (where 'a' is any positive interger, and 'n' > 1 is odd primeinteger) bulds a multitude one part of which is presented by prime numbers, and another by numbers  divisible by the members of arithmetic progression with increament '2n' - final result of sequential division is prime number.
n = 3 {7,13,19,25,...};
n=5 {11,21,31,41,...};
n = 7 {15,29,43,57,...};
but n=9 {7,13,19,25,...};
n = 11 {23,45,67,89,...}.

Programmaticaly I proved this statement for n = 3 and 'a' between 1 and 2000, for n = 5 and
'a' between 1 and 200, for n = 7 and 'a' between 1 and 100.

Last edited by mblacob1947 (2013-03-24 03:54:14)

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