78,557 (seventy-eight thousand five hundred [and] fifty-seven) is the natural number following 78,556 and preceding 78,558.
In mathematics The prime factorization of 78,557 is 17 * 4621, and both numbers are prime, meaning that 78,557 is a semiprime.
Sierpiński number
78557 is conjectured as the first, and smallest Sierpiński number. It was proved to be one by John Selfridge in the year 1962, who showed that all numbers of the form have a factor in the covering set }. But there are debates on whether 78557 is actually the smallest Sierpiński number. This is known as the Sierpiński problem.
To show that 78,557 really is the smallest Sierpiński number, one must show that all the odd numbers smaller than 78,557 are not Sierpiński numbers. That is, for every odd k below 78,557, there needs to exist a positive integer n such that is prime. The distributed volunteer computing project PrimeGrid is attempting to eliminate all the remaining values of k:
k = 21181, 22699, 24737, 55459, and 67607.
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