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257 (number)

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Title: 257 (number)  
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Subject: List of prime numbers, Fermat number, 256 (number), Pierpont prime, Full reptend prime
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257 (number)

256 257 258
Cardinal two hundred fifty-seven
Ordinal 257th
(two hundred and fifty-seventh)
Factorization 257
Prime yes
Roman numeral CCLVII
Binary 1000000012
Ternary 1001123
Quaternary 100014
Quinary 20125
Senary 11056
Octal 4018
Duodecimal 19512
Hexadecimal 10116
Vigesimal CH20
Base 36 7536

257 is the natural number between 256 and 258. It is also a prime number.

In mathematics

257 is a prime number of the form 2^{2^n}+1, 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]

It is also a balanced prime,[2] an irregular prime,[3] a prime that is one more than a square,[4] and a Jacobsthal–Lucas number,[5]

There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes).[6]

In other fields

257 is the country calling code for Burundi. See List of country calling codes.

References

  1. ^ Hsiung, C. Y. (1995), Elementary Theory of Numbers, Allied Publishers, pp. 39–40,  .
  2. ^ "Sloane's A006562 : Balanced primes", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ "Sloane's A000928 : Irregular primes", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ "Sloane's A002496 : Primes of form n^2 + 1", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ "Sloane's A014551 : Jacobsthal-Lucas numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ "Sloane's 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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