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

## List of notable prime numbers Edit

- 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.
- 5 is the second Fermat prime.
- 7 is the second Mersenne prime.
- 17 is the third Fermat 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 palindromic prime.**113**is a number following 112 and preceding 114. This number is prime.- 113 is also the 11th Sophie Germain prime.
^{[1]}

- 113 is also the 11th Sophie Germain prime.
**163**is the largest Heegner number.- 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-
**541**is the 100th prime.- The number
**563**is the largest known Wilson prime. - 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). **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.

- The number
**1,093**is the smallest Wieferich prime. - The number
**3,511**is the largest known Wieferich prime. **7,919**is the 1,000th prime.- The number
**16,843**is the smallest Wolstenholme 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**.^{[2]}- It is also the number of dominoes toppled on Friday, January 27, 1984 in Fürth.
^{[3]}

- It is also the number of dominoes toppled on Friday, January 27, 1984 in Fürth.
**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. - The number
**982,451,653**is the 50,000,000th prime number.^{[4]} - 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.^{[5]} **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).**10**is the first prime after a googol. This number has been named as "gooprol".^{100}+267- 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.^{77,232,917}-1

## Decimal expansions Edit

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

13324323309828620642589590565533923081483782150370704217672886885162756499559745515820505025366633291782689824970508202932981177480858933989443161914437860223829486481498201271806160710212419319981647591766471221549778791249081428838239687282350328447116067333733212653644768614482418519392989453221962115799024522405104498901459713737808685662443413595655349375239048341550958241450638814760944590236658374229179290977642222726256754317985049014925694253475958911625949983248927943732325461584057736439218050753700932773508299940797760652182226128976123104989251256067036990378850337686156071082494239176664863922935977210027442841831990203885909738423666863072782748227328328682294854519033727328136521782531700308411697804383954107548151069972793277926158786752065849297036891260767326465784518800758457811377420171439984071715181951117763117140248357060929148011779659503510742142318403354432945158174149891228101860550295710148830648133189336855311682287121680507578718514924229191266447187940645267114826510722293606459113473