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.