Primeval number

Primeval number

In mathematics, a primeval number is a natural number "n" for which the number of prime numbers which can be obtained by permuting all or some of its digits (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by Mike Keith.

The first few primeval numbers are:1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, ... OEIS|id=A072857The number of primes that can be obtained from the primeval numbers is:0, 1, 3, 4, 5, 7, 11, 14, 19, 21, 26, 29, ... (OEIS2C|id=A076497)The largest number of primes that can be obtained from a primeval number with "n" digits is:1, 4, 11, 31, 106, ... (OEIS2C|id=A076730)The smallest "n"-digit prime to achieve this number of primes is:2, 37, 137, 1379, 13679, ... (OEIS2C|id=A134596)

Primeval numbers can be composite. The first is 1037 = 17×61. A Primeval prime is a primeval number which is also a prime number::2, 13, 37, 107, 113, 137, 1013, 1237, 1367, 10079, ... (OEIS2C|id=A119535)

The following table shows the first six primeval numbers with the obtainable primes and the number of them.

See also

*Permutable prime
*Truncatable prime

External links

* [http://primes.utm.edu/glossary/page.php?sort=Primeval The Prime Glossary: Primeval number]
* [http://users.aol.com/s6sj7gt/primeval.htm "Integers Containing Many Embedded Primes" by Mike Keith]


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Primeval (disambiguation) — Primeval or Primæval means ancient or primitive . Primeval may also refer to:* Primeval forest, an area of forest that has attained great age * Primeval number, a positive integer satisfying certain conditions * Primeval (TV series), an ITV… …   Wikipedia

  • Primeval timeline — Primeval is an ongoing science fiction television series created by Adrian Hodges, who wrote the majority of the scripts, and Tim Haines of Impossible Pictures. It was produced by Haines and Cameron McAllister. It should be noted that in order to …   Wikipedia

  • Primeval Hunt — Infobox VG title = Primeval Hunt developer = Sega publisher = Sega designer = released = Arcade 2008 Xbox 360, Wii TBA genre = Shooter game,Hunting game modes = Single player, multiplayer cabinet = 29 Standard,62 Deluxe arcade system = Sega… …   Wikipedia

  • Primeval (film) — Infobox Film name = Primeval caption = Promotional movie poster for the film director = Michael Katleman producer = Gavin Polone writer = John D. Brancato, Michael Ferris starring = Dominic Purcell, Orlando Jones, Brooke Langton, Jürgen Prochnow …   Wikipedia

  • Primeval World — The Primeval World is a short attraction on the Disneyland Railroad at Disneyland in Anaheim, California. It comes immediately after the Grand Canyon between Tomorrowland Station and Main Street Station. At the Primeval World, you see a number of …   Wikipedia

  • Primeval (Doctor Who audio) — Bigfinishbox title=Primeval series= Doctor Who number=26 featuring=Fifth Doctor Nyssa writer=Lance Parkin director=Gary Russell producer=Gary Russell Jason Haigh Ellery executive producer=Jacqueline Rayner production code=6CD set between= The… …   Wikipedia

  • List of recreational number theory topics — This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins in challenging problems posed purely for their own sake. See list… …   Wikipedia

  • 113 (number) — ← 112 114 → 113 ← 110 111 112 113 114 115 116 …   Wikipedia

  • 137 (number) — 137 is the natural number following 136 and preceding 138. ← 136 138 → 137 ← 130 131 …   Wikipedia

  • List of Primeval characters — Primeval characters: Top   A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    References   External links …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”