307 (number)
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| ||||
|---|---|---|---|---|
| Cardinal | three hundred seven | |||
| Ordinal | 307th (three hundred seventh) | |||
| Factorization | prime | |||
| Prime | 63rd | |||
| Divisors | 1, 307 | |||
| Greek numeral | ΤΖ´ | |||
| Roman numeral | CCCVII | |||
| Binary | 1001100112 | |||
| Ternary | 1021013 | |||
| Senary | 12316 | |||
| Octal | 4638 | |||
| Duodecimal | 21712 | |||
| Hexadecimal | 13316 | |||
307 is the natural number following 306 and preceding 308.
In mathematics
[edit]- 307 is the 63rd prime number and 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 has class number 3.[8]
References
[edit]- ^ "Prime number information". mathworld.wolfram.com.
- ^ 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028818 (Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000293 (a(n) = number of solid (i.e., three-dimensional) partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006203 (Discriminants of imaginary quadratic fields with class number 3 (negated))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.