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307 (number)

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307 is the natural number following 306 and preceding 308.

307

List of numbers

← 0 100 200 300 400 500 600 700 800 900 →

three hundred seven

307th
(three hundred seventh)

63rd

1, 307

ΤΖ´

CCCVII

100110011₂

102101₃

1231₆

463₈

217₁₂

133₁₆

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

References

^ "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.

Retrieved from "https://en.wikipedia.org/w/index.php?title=307_(number)&oldid=1219609592" Last edited on 18 April 2024, at 20:00

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