Proth 4 Sierpinski

Sierpiński numbers are numbers where k !≡ 0 mod 4 for which k•4ⁿ+1 is composite for all natural numbers n and has a finite covering set of two or more distinct factors.

See also

• OEIS sequence A251057 is a subset of these numbers.

Table

There are 4 sequences in this Wiki:

k	Covering set
66741	[5, 7, 13, 17, 241]
157114	[5, 7, 13, 19, 37, 73]
190566	[5, 7, 13, 19, 73, 109]
271129	[5, 7, 13, 17, 241]

Proth primes

Miscellaneous

Proth prime Sierpiński problem Least n (k≤12)

Tables

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Categories

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Others

3k 15k 2145k 2805k 0 primes 100+ primes Sierpiński numbers Missing ranges

Other categories

Sierpiński numbers Missing ranges Low weight Count 0

Other bases

3 4 5 6 7 11 999