307 (number)
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | three hundred seven | |||
| Ordinal | 307th (three hundred seventh) | |||
| Factorization | prime | |||
| Divisors | 1, 307 | |||
| Greek numeral | ΤΖ´ | |||
| Roman numeral | CCCVII | |||
| Binary | 1001100112 | |||
| Ternary | 1021013 | |||
| Quaternary | 103034 | |||
| Quinary | 22125 | |||
| Senary | 12316 | |||
| Octal | 4638 | |||
| Duodecimal | 21712 | |||
| Hexadecimal | 13316 | |||
| Vigesimal | F720 | |||
| Base 36 | 8J36 | |||
307 is the natural number following 306 and preceding 308.
In mathematics
- 307 is an odd prime number.[1] It is an isolated (i.e., not twin) prime,[2] but because 309 is a semiprime, 307 is a Chen prime.[3][4]
- 307 is the number of one-sided noniamonds meaning that it is the number of ways to organize 9 triangles with each one touching at least one other on the edge.[5]
- 307 is the third non-palindromic number to have a palindromic square. 3072=94249.[6]
- 307 is the number of solid partitions of 7.[7]
- 307 is one of only 16 natural numbers for which the imaginary quadratic field [math]\displaystyle{ \mathbb{Q}(\sqrt{-n}) }[/math] has class number 3.[8]
References
- ↑ "Prime number information". https://mathworld.wolfram.com/PrimeNumber.html.
- ↑ Sloane, N. J. A., ed. "Sequence A007510 (Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime)". OEIS Foundation. https://oeis.org/A007510.
- ↑ Sloane, N. J. A., ed. "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime)". OEIS Foundation. https://oeis.org/A109611.
- ↑ Lewulis, Pawel (2016). "Chen primes in arithmetic progressions". arXiv:1601.02873 [math.NT].
- ↑ Sloane, N. J. A., ed. "Sequence A006534 (Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed)". OEIS Foundation. https://oeis.org/A006534.
- ↑ Sloane, N. J. A., ed. "Sequence A028818 (Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots)". OEIS Foundation. https://oeis.org/A028818.
- ↑ Sloane, N. J. A., ed. "Sequence A000293 (a(n) = number of solid (i.e., three-dimensional) partitions of n)". OEIS Foundation. https://oeis.org/A000293.
- ↑ Sloane, N. J. A., ed. "Sequence A006203 (Discriminants of imaginary quadratic fields with class number 3 (negated))". OEIS Foundation. https://oeis.org/A006203.
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