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References
257 (number)
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From Wikipedia, the free encyclopedia
257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 258.
257 is a prime number of the form
specifically with n = 3, and therefore a Fermat prime. Thus a regular polygon with 257 sidesisconstructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.[1]
Analogously, 257 is the third Sierpinski prime of the first kind, of the form
➜
.[2]
It is also
a balanced prime,[3]anirregular prime,[4]
a prime that is one more than a square,[5]
and a Jacobsthal–Lucas number.[6]
Four-fold 257 is 1028, which is the prime index of the fifth Mersenne prime, 8191.[7][8]
There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (orpolyhedral graphs with eight nodes).[9]
References
[edit]
^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002496 (Primes of form n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A014551 (Jacobsthal-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-21.
^ Sloane, N. J. A. (ed.). "Sequence A000668 (Mersenne primes (primes of the form 2^n - 1).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-21.
^ Sloane, N. J. A. (ed.). "Sequence A000944 (Number of polyhedra (or 3-connected simple planar graphs) with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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100,000
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1,000,000
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10,000,000
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100,000,000
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1,000,000,000
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Retrieved from "https://en.wikipedia.org/w/index.php?title=257_(number)&oldid=1209309999"
Category:
●Integers
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