307 (number)

← 306 307 308 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred seven
Ordinal	307th (three hundred seventh)
Factorization	prime
Prime	63rd
Divisors	1, 307
Greek numeral	ΤΖ´
Roman numeral	CCCVII, 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

• 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 ${\displaystyle \mathbb {Q} ({\sqrt {-n}})}$ has class number 3. ^[8]

References

1. "Prime number information". mathworld.wolfram.com.
2. Sloane, N. J. A. (ed.). "SequenceA007510(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.
3. Sloane, N. J. A. (ed.). "SequenceA109611(Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Lewulis, Pawel (2016). "Chen primes in arithmetic progressions". arXiv: 1601.02873 [math.NT].
5. Sloane, N. J. A. (ed.). "SequenceA006534(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.
6. Sloane, N. J. A. (ed.). "SequenceA028818(Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
7. Sloane, N. J. A. (ed.). "SequenceA000293(a(n) = number of solid (i.e., three-dimensional) partitions of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
8. Sloane, N. J. A. (ed.). "SequenceA006203(Discriminants of imaginary quadratic fields with class number 3 (negated))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.