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Substring sums of prime concatenations

Published on Sunday, 14th May 2017, 01:00 am; Solved by 306;
Difficulty rating: 45%

Problem 603

Let $S(n)$ be the sum of all contiguous integer-substrings that can be formed from the integer $n$. The substrings need not be distinct.

For example, $S(2024) = 2 + 0 + 2 + 4 + 20 + 02 + 24 + 202 + 024 + 2024 = 2304$.

Let $P(n)$ be the integer formed by concatenating the first $n$ primes together. For example, $P(7) = 2357111317$.

Let $C(n, k)$ be the integer formed by concatenating $k$ copies of $P(n)$ together. For example, $C(7, 3) = 235711131723571113172357111317$.

Evaluate $S(C(10^6, 10^{12}))$ mod $(10^9 + 7)$.