43,112,609 (number)

From HandWiki

43,112,609 (forty-three million, one hundred twelve thousand, six hundred nine) is the natural number following 43,112,608 and preceding 43,112,610.

Short description: Natural number
43112609
Cardinalforty-three million one hundred twelve thousand six hundred nine
Ordinal43112609th
(forty-three million one hundred twelve thousand six hundred ninth)
Factorizationprime
Greek numeral[math]\displaystyle{ \stackrel{\delta\tau\iota\alpha}{\Mu} }[/math]͵βχθ´
Roman numeralN/A
Binary101001000111011000101000012
Ternary100000101001010223
Quaternary22101312022014
Quinary420141004145
Senary41400152256
Octal2443542418
Duodecimal1253151512
Hexadecimal291D8A116
VigesimalD991A920
Base 36PO1WH36

In mathematics

43,112,609 is a prime number. Moreover, it is the exponent of the 47th Mersenne prime, equal to M43,112,609 = 243,112,609 − 1, a prime number with 12,978,189 decimal digits. It was discovered on August 23, 2008 by Edson Smith, a volunteer of the Great Internet Mersenne Prime Search.[1] In a remarkable coincidence, this Mersenne prime holds the record for the one with the closest subsequently discovered Mersenne primes, both in terms of size and in terms of chronological order. The 45th Mersenne prime, M37,156,667 = 237,156,667 − 1, was discovered two weeks later on September 6, 2008, marking the shortest chronological gap between discoveries of Mersenne primes since the formation of the online collaborative project in 1996. It was the first time since 1963 when two Mersenne primes were discovered less than 30 days apart from each other. Less than a year later, on June 4, 2009, the 46th Mersenne prime, M42,643,801 = 242,643,801 − 1, was discovered by Odd Magnar Strindmo, a GIMPS participant from Norway .[2] The result for this prime was first reported to the server in April 2009, but due to a bug, remained unnoticed for nearly two months.[3] Having 12,837,064 decimal digits, it is only 141,125 digits, or 1.09%, shorter than M43,112,609, which remained largest known prime number until the discovery of M57,885,161 = 257,885,161 − 1 in late January 2013.

43,112,609 is the degree of four of the seven largest primitive binary trinomials over GF(2) found in 2016.[4] and were the four largest in 2011.[5]

43,112,609 is a Sophie Germain prime, the largest of only eight known Mersenne prime indexes to have this property.[6]

43,112,609 is not a Gaussian prime, the largest of only 28 known Mersenne prime indexes to have this property.[7]

References

Further reading