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307 (number)

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Short description: Natural number
← 306 307 308 →
Cardinalthree hundred seven
Ordinal307th
(three hundred seventh)
Factorizationprime
Divisors1, 307
Greek numeralΤΖ´
Roman numeralCCCVII
Binary1001100112
Ternary1021013
Quaternary103034
Quinary22125
Senary12316
Octal4638
Duodecimal21712
Hexadecimal13316
VigesimalF720
Base 368J36

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

  1. ↑ "Prime number information". https://mathworld.wolfram.com/PrimeNumber.html. 
  2. ↑ 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. 
  3. ↑ 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. 
  4. ↑ Lewulis, Pawel (2016). "Chen primes in arithmetic progressions". arXiv:1601.02873 [math.NT].
  5. ↑ 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. 
  6. ↑ 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. 
  7. ↑ 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. 
  8. ↑ 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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