(UNICAMP - 2019 - 1ª FASE)
Largest prime number discovered: with more than 23m digits
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.
Adaptado de Ian Sample, “Largest prime number discovered: with more than 23m digits”. The Guardian, 04/ 01/2018.
Considerando as informações contidas no excerto anterior, qual dos números a seguir é um primo de Mersenne?
23.
29.
31.
37.
Gabarito:
31.
De acordo com o texto, o número primo de Mersenne tem as seguintes características:"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" (Como qualquer número primo, um primo de Mersenne é divisível somente por si mesmo e por um, mas é derivado pela multiplicação de dois juntos várias vezes antes de se remover um). Sendo assim, o número primo de Mersenne é encontrado através do cálculo 2n- 1. A alternativa C apresenta o número 31, que é o resultado de 25 - 1.