The smoothness of a number is its maximal prime factor. The number has smoothness 83, has smoothness 37, and has smoothness 97. All three numbers can be considered to be 97-smooth as well, since and . Multiplied out, these numbers are 7496643, 7496644, and 7496645, making this a consecutive 97-smooth triplet.
For a given prime , all consecutive -smooth pairs can be found via Størmer's method . For this Demonstration, all 97-smooth pairs were found. The number 97 is the prime. There are subsets of these primes. The products of these subsets form the value in the Pell equation . All of these equations were analyzed, with 21805 prime subsets yielding solutions. For smoothnesses above 97, solutions will be missing.
The largest proven maximal consecutive smooth pair is and .