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Gigantic prime

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A gigantic prime is a prime number with at least 10,000 decimal digits.

The term appeared in Journal of Recreational Mathematics in the article "Collecting gigantic and titanic primes" (1992) by Samuel Yates. Chris Caldwell, who continued Yates' collection in The Prime Pages, reports that he changed the requirement from Yates' original 5,000 digits to 10,000 digits, when he was asked to revise the article after the death of Yates.[1] Few primes of that size were known then, but a modern personal computer can find many in a day.

First discoveries[edit]

The first discovered gigantic prime was the Mersenne prime 244497 − 1. It has 13,395 digits and was found in 1979 by Harry L. Nelson and David Slowinski.[2]

The smallest gigantic prime is 109999 + 33603.[3] It was proved prime in 2003 by Jens Franke, Thorsten Kleinjung and Tobias Wirth with their own distributed ECPP program. It was the largest ECPP proof at the time.

The first gigantic primes are 109999 + n for n = 33603, 55377, 70999, 78571, 97779, 131673, 139579, 236761, 252391, 282097, 333811, 342037, 355651, 359931, 425427, 436363, 444129, 473143, 479859, 484423, 515787, 543447, 680979, 684273, 709053, 709431, 780199, 781891, 788527, 813019, ... (sequence A142587 in the OEIS)

The first discovered gigantic twin prime was the 11,713-digit 242206083 × 238880 ± 1, found by Karl-Heinz Indlekofer and Antal Járai in 1995.[4][5]

The first discovered gigantic prime triplet was the 10,047-digit 2072644824759 × 233333 + d for d = −1, +1, +5, found by Norman Luhn and François Morain in 2008.[6][7]

See also[edit]

  • Titanic prime – at least 1,000 digits
  • Megaprime – at least a million digits
  • Largest known prime number

References[edit]

  1. http://primes.utm.edu/references/refs.cgi?long=Yates92b
  2. http://primes.utm.edu/notes/by_year.html
  3. http://factordb.com/index.php?id=1100000000081719528
  4. "PrimePage Primes: 242206083·2^38880 - 1". PrimePages. Retrieved 1 May 2021.
  5. Indlekofer, Karl-Heinz; Járai, Antal (16 February 1999). "Largest known twin primes and Sophie Germain primes". Mathematics of Computation. 68 (227): 1317–1325. doi:10.1090/S0025-5718-99-01079-0.
  6. "2072644824759·2^33333 + 5". PrimePages. Retrieved 1 May 2021.
  7. "Prime Curios! 35429...67327 (10047-digits)". PrimePages.

External links[edit]

fr:Nombre premier#Jalons symboliques


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