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==In mathematics== |
==In mathematics== |
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191 is a [[prime number]], part of a [[prime quadruplet]] of four [[prime number|primes]]: 191, [[193 (number)|193]], [[197 (number)|197]], and [[199 (number)|199]]. Because doubling and adding one produces another prime number (383), 191 is a [[Sophie Germain prime]]. It is the smallest prime that is not a [[full reptend prime]] in ''any'' base from 2 to 10 |
191 is a [[prime number]], part of a [[prime quadruplet]] of four [[prime number|primes]]: 191, [[193 (number)|193]], [[197 (number)|197]], and [[199 (number)|199]].<ref>{{Cite OEIS|A136162|List of prime quadruplets {p, p+2, p+6, p+8} }}</ref> Because doubling and adding one produces another prime number (383), 191 is a [[Sophie Germain prime]].<ref>{{Cite OEIS|A005384|Sophie Germain primes p: 2p+1 is also prime}}</ref> It is the smallest prime that is not a [[full reptend prime]] in ''any'' base from 2 to 10; in fact, the smallest base for which 191 is a full period prime is [[base 19]].<ref>Wolfram MathWorld; [http://mathworld.wolfram.com/PrimitiveRoot.html Primitive Root]</ref> |
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==See also== |
==See also== |
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Revision as of 09:27, 21 August 2022
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|---|---|---|---|---|
| Cardinal | one hundred ninety-one | |||
| Ordinal | 191st (one hundred ninety-first) | |||
| Factorization | prime | |||
| Prime | yes | |||
| Greek numeral | ΡϞΑ´ | |||
| Roman numeral | CXCI | |||
| Binary | 101111112 | |||
| Ternary | 210023 | |||
| Senary | 5156 | |||
| Octal | 2778 | |||
| Duodecimal | 13B12 | |||
| Hexadecimal | BF16 | |||
191 (one hundred [and] ninety-one) is the natural number following 190 and preceding 192.
In mathematics
191 is a prime number, part of a prime quadruplet of four primes: 191, 193, 197, and 199.[1] Because doubling and adding one produces another prime number (383), 191 is a Sophie Germain prime.[2] It is the smallest prime that is not a full reptend prime in any base from 2 to 10; in fact, the smallest base for which 191 is a full period prime is base 19.[3]
See also
References
- ^ Sloane, N. J. A. (ed.). "Sequence A136162 (List of prime quadruplets {p, p+2, p+6, p+8})". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Wolfram MathWorld; Primitive Root
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