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281 (number)

From Wikipedia, the free encyclopedia
Natural number
← 280281 282 →
Cardinaltwo hundred eighty-one
Ordinal281st
(two hundred eighty-first)
Factorizationprime
Prime60th
Greek numeralΣΠΑ´
Roman numeralCCLXXXI,cclxxxi
Binary1000110012
Ternary1011023
Senary11456
Octal4318
Duodecimal1B512
Hexadecimal11916

281 is thenatural number following280 and preceding282. It is also aprime number.

In mathematics

[edit]

281 is atwin prime with 283,[1]Sophie Germain prime,[2] sum of the first fourteen primes, sum of seven consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53),Chen prime,[3]Eisenstein prime with no imaginary part, and acentered decagonal number.[4]

281 is the smallest primep such that thedecimalperiod length of thereciprocal ofp is (p−1)/10, i.e. the period length of 1/281 is 28. However, inbinary, it has period length 70.

The generalizedrepunit number281p1280{\displaystyle {\frac {281^{p}-1}{280}}} iscomposite for all primep < 60000.

References

[edit]
  1. ^Sloane, N. J. A. (ed.)."Sequence A001359 (Lesser of twin primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A109611 (chen prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A062786 (centered 10-gonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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