Largest prime number discovered: with more than 23m – UNICAMP 2019 

Largest prime number discovered: with more than 23m digits

(Adaptado de Ian Sample, “Largest prime number discovered: with more than 23m digits”. The Guardian, 04/ 01/2018.)

Known simply as M77232917, the figure is arrived at by calculating two to the power of 77,232,917 and subtracting one, leaving a gargantuan string of 23,249,425 digits. The result is nearly one million digits longer than the previous record holder discovered in January 2016. The number belongs to a rare group of so-called Mersenne prime numbers, named after the 17th century French monk Marin Mersenne. Like any prime number, a Mersenne prime is divisible only by itself and one, but is derived by multiplying twos together over and over before taking away one. The previous record-holding number was the 49th Mersenne prime ever found, making the new one the 50th.

Considerando as informações contidas no excerto anterior, qual dos números a seguir é um primo de Mersenne?

(A) 23.

(B) 29.

(C) 31.

(D) 37.

Resposta:

Alternativa Correta: C) 31.

Das alternativas apresentadas, somente 31 é um primo de Mersenne, pois
31 = 32 – 1 = 2 . 2 . 2 . 2 . 2 – 1