A prime number is an integer greater than 1 that has no divisors other than 1 and itself.

## List of notable prime numbers

**2**is the smallest prime and the only even prime.**3**is the only number that is both a Mersenne prime and a Fermat prime. It is also the first odd prime.**5**is the second Fermat prime.**7**is the second Mersenne prime.**17**is the third Fermat prime and the third Stern prime.**31**is the third Mersenne prime.**101**is the smallest 3-digit prime. It's also a twin prime with 103. 101 is also a centered decagonal number and a palindromic prime.**113**is a Sophie Germain prime.^{[1]}- It is also is the sum of the hyperfactorials of the first three positive numbers.
- Furthermore, \(\frac{355}{113}\) is a famous approximation of \(\pi\) named Milü. It's equal to 3.141592920...

**131**is a palindromic permutable prime.**137**is a centered polygonal number and the fifth largest known Stern prime.- It is also approximately the reciprocal of the fine-structure constant.
- Since 177 and 183 kHz are also used as AM radio carriers, there are
**137**AM radio frequencies in Europe. - With a leading zero, it is also the German mass traffic telephone number prefix.

**151**is a centered decagonal number and a palindromic prime.- It is also the last number
*n*, such that e^{n}is smaller than the first noncanonical -illion. - Furthermore, in Orthodox churches, the Book of Psalms contains
**151**psalms. - Finally, it is also the number of species in the first Pokémon generation.

- It is also the last number
**163**is the largest Heegner number. For this reason, it has been used in the Ramanujan constant.- The McKay-Thompson series of monstrous moonshine span a 163-dimensional vector space.
- It is also the number of white pips in a Chinese domino set.

- The emirp
**167**is the first number*n*, such that 4^{n}is larger than a googol. **181**is a centered square number, a centered pentagonal number, a palindromic prime and a star prime.**191**is a centered polygonal number, a palindromic prime and a Thabit prime.- It is also the number of non-control ISO/IEC 8859 characters.

**193**is a cuban prime, a Pierpont prime, a Proth prime, and the number of ways to add seven ordinals.**199**is a centered triangular number, a Lucas prime and a permutable prime.- Since it is one less than 200, it is often used as a price, or as a part of a price.

**211**is a centered decagonal number, a centered polygonal number and a prime Euclid number.**227**is the fourth largest known Stern prime.- It is also the number of pips in a Chinese domino set.

**239**is a Sophie Germain prime. It was the PEGG value on May 22nd, 2017.- Since 239
^{2}+ 1 = 2 × 13^{4}, it also appears in many Machin-like formulae. - It is the largest integer which cannot be written as a sum of eight nonnegative cubes; the only other nonnegative integer with this property is 23.
- It is also one of only seven nonnegative integers which cannot be written as a sum of eighteen fourth powers; the largest integer with this property is 559.

- Since 239
- The number
**257**is a Fermat prime \(2^{2^3}+1\).- The isotope fermium-
**257**is the heaviest nuclide that can be formed by neutron capture from naturally occuring elements.

- The isotope fermium-
- The number
**271**is a cuban prime, and the only prime house number. **277**is a centered polygonal number and a Perrin prime.**311**is a permutable prime and a right-truncatable prime.**313**is a centered square number and a palindromic prime.**317**is an index of a repunit prime and a two-sided prime.**337**is a left-truncatable prime, a permutable prime and a quartan prime.**353**is a palindromic Proth prime.**373**is a palindromic permutable prime.**383**is a palindromic prime, a Thabit prime and a Woodall prime.**409**is a minimal prime.- Since it is the integral part of the quotient of the DVD sector size (2 KiB) by the 40-bit key size, it is also the number of keys in the CSS disk-key-block.

- The number
**443**has been used in the definition of the triangrolplex. **449**is a minimal prime, a Proth prime, and the number of ways to add eight ordinals.**499**is a minimal prime.- Since it is one less than 500, it is often used as a price, or as a part of a price.

**541**is the 100th prime.- The number
**563**is the largest known Wilson prime. **613**is a centered square number and a left-truncatable prime.- It is also the number of commandments in Judaism.

**619**is an alternating factorial prime and a strobogrammatic prime.**709**is an emirp.- A method for generating a sequence of primes is to start with 1, then choosing the smallest prime successor of a multiple of the previous number in each step. The compositeness can be easily certified by Fermat or Miller-Rabin, and the primality by Pratt. The resulting sequence starts with 1, 2, 3, 7, 29, 59, 709, … (OEIS A061092).
- Another method for generating a sequence of primes is to start with 1, then choosing the
*n*-th prime, where*n*is the previous number. But this sequence is harder to calculate. It starts with 1, 2, 3, 5, 11, 31, 127, 709, … (OEIS A007097). - Furthermore, it is the largest number
*n*, for which e^{n}can be represented in the double-precision floating-point format. - Finally, it is the number of seats in the 19th Bundestag, which is the largest democratically elected national parliament house ever.

**719**is a prime number. As 119, 121 and 721 are all composite, it is the only 3-digit factorial prime.- It is also the number of hours in a 30-day month (April, June, September or November) containing a spring DST transition.

**727**is a palindromic prime.**733**is a permutable prime and a right-truncatable prime.**757**is a Hogben number and a palindromic prime.**773**is a tetranacci number and the only 3-digit restricted left-truncatable prime.**787**is a palindromic prime.- The number
**797**is the largest palindromic right-truncatable prime and the largest palindromic two-sided prime. **881**is a minimal prime and a quartan prime.- The number
**919**is a cuban prime, and the largest known non-repunit palindromic permutable prime. **929**is a palindromic Proth prime.**977**is the third largest known Stern prime.- The number
**991**is a centered polygonal number, a minimal prime and the largest known non-repunit permutable prime. - The number
**1,093**is the smallest Wieferich prime. **1,187**and**1,493**are the two largest known Stern primes.**1,597**is a Fibonacci prime and a pancake number.**2,311**is a centered decagonal number and a prime Euclid number.**3,137**is a two-sided prime.- The number
**3,511**is the largest known Wieferich prime. **3,797**is a two-sided prime.**6,469**and**6,949**are minimal primes.**7,919**is the 1,000th prime.**9,001**is a minimal prime.- It also refers to the "it’s over 9000" Internet meme.
^{[2]}

- It also refers to the "it’s over 9000" Internet meme.
**9,049**,**9,649**and**9,949**are minimal primes.**14,197**is a pancake number and a Perrin prime.- The number
**16,843**is the smallest Wolstenholme prime.^{[3]}^{[4]} **42,841**is a cuban prime and a star prime.**60,649**is the only 5-digit minimal prime.- \(65,537=2^{2^4}+1\) is the largest known Fermat prime.
**148,091**is the largest known number*n*for which both F(*n*) and L(*n*) are probable prime numbers.- The number
**262,657**is one of only four known Mersenne–Fermat primes, which are neither Fermat nor Mersenne primes. - By fitting the least-degree polynomial to the first
*n*odd primes, one can attempt to guess the (*n*+ 1)-st odd prime, but this will give almost always incorrect results, which can be prime or composite, and positive or negative. The absolute value of the first negative prime obtained in this way is equal to**281,581**.^{[5]}- It is also the number of dominoes toppled on Friday, January 27, 1984 in Fürth.
^{[6]}

- It is also the number of dominoes toppled on Friday, January 27, 1984 in Fürth.
- The number
**294,001**is the smallest weakly prime. **666,649**is a minimal prime.- The number
**739,397**is the largest two-sided prime. **946,669**is a minimal prime.- The number
**999,331**is the largest known non-repunit circular prime. **999,983**is the largest prime number smaller than 1,000,000; and, as such, the largest Class 1 number to be prime.**1,000,003**is the smallest prime number larger than 1,000,000; and, as such, the smallest Class 2 number to be prime.- The number
**2,124,679**is the largest known Wolstenholme prime.^{[3]}^{[4]} - The numbers
**60,000,049**,**66,000,049**and**66,600,049**are the three largest minimal primes. - The number
**73,939,133**is the largest right-truncatable prime. - The number
**799,636,997**is the largest palindromic left-truncatable prime and the largest palindromic truncatable prime. - The number
**982,451,653**is the 50,000,000th prime number.^{[7]} **1,679,457,781**and**1,938,092,824,081**are cuban primes and star primes.- The number
**4,432,676,798,593**is one of only four known Mersenne–Fermat primes, which are neither Fermat nor Mersenne primes. - The number
**29,996,224,275,833**is the 1,000,000,000,000th prime number.^{[8]} **9,007,199,254,740,881**is a positive integer equal to \(2^{53} - 111\). It is notable in computer science for being the largest prime number which can be represented exactly in the`double`

floating-point format (which has a 53-bit significand).- The number
**357,686,312,646,216,567,629,137**is the largest left-truncatable prime. **10**is the first prime after a googol. This number has been named as "gooprol".^{100}+267**10**is the smallest titanic prime.^{999}+7- The number \(\frac{10^{1,031}-1}{9}\) is the the largest known base 10 repunit prime.
- The number \(\frac{2^{3,481}-1}{2^{59}-1}\) is one of only four known Mersenne–Fermat primes that are neither Fermat nor Mersenne primes.
- Both of the last two primes have 1,031 digits, and start with the digit “1”.

- The number
**10**is the largest known emirp.^{10,006}+941,992,101×10^{4,999}+1 - The number
**2,618,163,402,417×2**is the largest known Sophie Germain prime.^{1,290,000}-1 - The numbers
**2,996,863,034,895×2**are the largest known twin primes.^{1,290,000}±1 - The number
**2**is the largest known prime as of December 2020.^{82,589,933}-1

## Decimal expansions

For \(\frac{2^{3,481}-1}{2^{59}-1}\):

13324323309828620642589590565533923081483782150370704217672886885162756499559745515820505025366633291782689824970508202932981177480858933989443161914437860223829486481498201271806160710212419319981647591766471221549778791249081428838239687282350328447116067333733212653644768614482418519392989453221962115799024522405104498901459713737808685662443413595655349375239048341550958241450638814760944590236658374229179290977642222726256754317985049014925694253475958911625949983248927943732325461584057736439218050753700932773508299940797760652182226128976123104989251256067036990378850337686156071082494239176664863922935977210027442841831990203885909738423666863072782748227328328682294854519033727328136521782531700308411697804383954107548151069972793277926158786752065849297036891260767326465784518800758457811377420171439984071715181951117763117140248357060929148011779659503510742142318403354432945158174149891228101860550295710148830648133189336855311682287121680507578718514924229191266447187940645267114826510722293606459113473

## See also

## Sources

- ↑ OEIS, Sequence A005384 (accessed 2020-11-22)
- ↑ Cloudy's large number list Part 2 - Cloudy's googology
- ↑
^{3.0}^{3.1}OEIS A088164 - ↑
^{4.0}^{4.1}Prime Curios!: 16843 - ↑ OEIS A140118
- ↑ Prime Curios!: 281581
- ↑ The first fifty million primes.
*The Prime Pages*. - ↑ The Prime Database: The Nth Prime Page

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