FACT #25
The largest known prime number (as of August 2019) is
282,589,933 − 1, a number which has 24,862,048 digits when written in base 10.
It was found by Patrick Laroche of the Great Internet Mersenne Prime Search
(GIMPS) in 2018.
A 2016 plot of the number of digits in largest known prime
by year, since the electronic computer. The vertical scale is logarithmic. The
red line is the exponential curve of best fit: y = exp(0.187394 t − 360.527),
where t is in years.
A prime number is a number with no divisors other than 1
and itself. Euclid proved that there is no largest prime number, and many
mathematicians and hobbyists continue to search for large prime numbers.
Many of the largest known primes are Mersenne primes,
numbers that are one less than a power of two. As of December 2018, the eight
largest known primes are Mersenne primes. The last seventeen record primes were
Mersenne primes.
The fast Fourier transform implementation of the
Lucas–Lehmer primality test for Mersenne numbers is fast compared to other
known primality tests for other kinds of numbers.
The record is currently held by 282,589,933 − 1
with 24,862,048 digits, found by GIMPS in December 2018. Its value is:
148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560
...
(24,861,808 digits omitted)
...
062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591
The first and last 120 digits are shown above
FACT #25
Reviewed by Admin
on
September 18, 2019
Rating:
Reviewed by Admin
on
September 18, 2019
Rating:
