π sequences
Problem 609
For every the prime-counting function is equal to the number of primesnot exceeding .
E.g. and .
E.g. and .
We say that a sequence of integers is a sequence if
For there are three distinct sequences: (10,4), (10,4,2) and (10,4,2,1).
Let be the number of elements of that are not prime.
Let be the number of sequences for which and .
Let be the product of all that are larger than 0.
You are given: P(10)=3×8×9×3=648 and P(100)=31038676032.
Let be the number of sequences for which and .
Let be the product of all that are larger than 0.
You are given: P(10)=3×8×9×3=648 and P(100)=31038676032.
Find . Give your answer modulo 1000000007.