// Workers AI · dad joke modeIs 78,557 a large number? It's a big digit-al.

← 78556 78557 78558 →
List of numbers Integers ← 0 10k 20k 30k 40k 50k 60k 70k 80k 90k →
Cardinal	seventy-eight thousand five hundred fifty-seven
Ordinal	78557th (seventy-eight thousand five hundred fifty-seventh)
Factorization	17 × 4621
Divisors	1, 17, 4621, 78557
Greek numeral	${\stackrel {\zeta }{\mathrm {M} }}$͵ηφνζ´
Roman numeral	LXXVMMMDLVII, lxxvmmmdlvii
Binary	100110010110111012
Ternary	102222021123
Senary	14034056
Octal	2313358
Duodecimal	3956512
Hexadecimal	132DD16

78,557 (seventy-eight thousand five hundred [and] fifty-seven) is the natural number following 78,556 and preceding 78,558.

In mathematics

Sierpiński number

Unsolved problem in mathematics

Is 78,557 the smallest Sierpiński number?

More unsolved problems in mathematics

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 78557⋅2ⁿ + 1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. 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 k2ⁿ + 1 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.