Gigantic prime

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]

References[edit]

↑ http://primes.utm.edu/references/refs.cgi?long=Yates92b
↑ http://primes.utm.edu/notes/by_year.html
↑ http://factordb.com/index.php?id=1100000000081719528
↑ "PrimePage Primes: 242206083·2^38880 - 1". PrimePages. Retrieved 1 May 2021.
↑ 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.
↑ "2072644824759·2^33333 + 5". PrimePages. Retrieved 1 May 2021.
↑ "Prime Curios! 35429...67327 (10047-digits)". PrimePages.

External links[edit]

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fr:Nombre premier#Jalons symboliques

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[1] ttp://primes.utm.edu/references/refs.cgi?long=Yates92b

[2] ttp://primes.utm.edu/notes/by_year.html

[3] ttp://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.

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v t e Prime number classes
By formula	Fermat ( $2 2 n + 1$ ) Mersenne ( $2 p - 1$ ) Double Mersenne ( $2 2 p -1 - 1$ ) Wagstaff $(2 p + 1)/3$ Proth ( $k \cdot2 n + 1$ ) Factorial ( $n! \pm 1$ ) Primorial ( $p n # \pm 1$ ) Euclid ( $p n # + 1$ ) Pythagorean ( $4 n + 1$ ) Pierpont ( $2 m \cdot3 n + 1$ ) Quartan ( $x 4 + y 4$ ) Solinas ( $2 m \pm 2 n \pm 1$ ) Cullen ( $n \cdot2 n + 1$ ) Woodall ( $n \cdot2 n - 1$ ) Cuban ( $x 3 - y 3)/(x - y$ ) Carol $(2 n - 1) 2 - 2$ Kynea $(2 n + 1) 2 - 2$ Leyland ( $x y + y x$ ) Thabit ( $3\cdot2 n - 1$ ) Williams ( $(b -1)\cdot b n - 1$ ) Mills ( $⌊ A 3 n ⌋$ )
By integer sequence	Fibonacci Lucas Pell Newman–Shanks–Williams Perrin Partitions Bell Motzkin
By property	Wieferich (pair) Wall–Sun–Sun Wolstenholme Wilson Lucky Fortunate Ramanujan Pillai Regular Strong Stern Supersingular (elliptic curve) Supersingular (moonshine theory) Good Super Higgs Highly cototient
Base-dependent	Happy Dihedral Palindromic Emirp Repunit $(10 n - 1)/9$ Permutable Circular Truncatable Strobogrammatic Minimal Weakly Full reptend Unique Primeval Self Smarandache–Wellin Tetradic
Patterns	Twin ( $p, p + 2$ ) Bi-twin chain ( $n - 1, n + 1, 2 n - 1, 2 n + 1, \dots$ ) Triplet ( $p, p + 2 or p + 4, p + 6$ ) Quadruplet ( $p, p + 2, p + 6, p + 8$ ) k−Tuple Cousin ( $p, p + 4$ ) Sexy ( $p, p + 6$ ) Chen Sophie Germain ( $p, 2 p + 1$ ) Cunningham ( $p, 2 p \pm 1, 4 p \pm 3, 8 p \pm 7, ...$ ) Safe ( $p, (p - 1)/2$ ) Arithmetic progression ( $p + a\cdotn, n = 0, 1, 2, 3, ...$ ) Balanced ( $consecutive p - n, p, p + n$ )
By size	Titanic (1,000+ digits) Gigantic (10,000+ digits) Mega (1,000,000+ digits) Largest known
Complex numbers	Eisenstein prime Gaussian prime
Composite numbers	Pseudoprime Catalan Elliptic Euler Euler–Jacobi Fermat Frobenius Lucas Somer–Lucas Strong Carmichael number Almost prime Semiprime Interprime Pernicious
Related topics	Probable prime Industrial-grade prime Illegal prime Formula for primes Prime gap
First 60 primes	2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
List of prime numbers

Gigantic prime

Contents

First discoveries[edit]

See also[edit]

References[edit]

External links[edit]

📰 Article(s) of the same category(ies)[edit]