Two Consecutive Integers each Product of Four Distinct Primes

Theorem

The sequence of pairs of consecutive positive integers which are each the product of exactly $4$ distinct prime numbers begins:

$\tuple {7314, 7315}, \tuple {8294, 8295}, \tuple {8645, 8646}, \tuple {9009, 9010}, \ldots$

The sequence of the first elements is A140078 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

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Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $7314$