Limit inferior of difference of consecutive primes was 70 million

Probability Level 4

A×B×C×D×E×F=7×107 \large A \times B \times C \times D \times E \times F = 7 \times 10^7

Determine the number of ordered solutions for integers A,B,C,D,E,FA,B,C,D,E,F such that they satisfy the equation above.

Inspiration.

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