From Wikipedia, the free encyclopedia
Natural number
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 sides is
constructible 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]
an
irregular 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 (or
polyhedral graphs with eight nodes).
[9]
References
-
^ Hsiung, C. Y. (1995),
Elementary Theory of Numbers, Allied Publishers, pp. 39–40,
ISBN
9788170234647.
-
^ Weisstein, Eric W.
"Sierpiński Number of the First Kind". mathworld.wolfram.com. Retrieved 2020-07-30.
-
^
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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