Problem 216
Investigating the primality of numbers of the form 2n2-1
Consider numbers t(n) of the form t(n) = 2n2-1 with n > 1.
The first such numbers are 7, 17, 31, 49, 71, 97, 127 and 161.
It turns out that only 49 = 7*7 and 161 = 7*23 are not prime.
For n ≤ 10000 there are 2202 numbers t(n) that are prime.
How many numbers t(n) are prime for n ≤ 50,000,000 ?
研究形如2n2-1的数是否为素数
考虑形如t(n) = 2n2-1的数t(n)，其中n > 1。
前几个这样的数分别是7、17、31、49、71、97、127和161。
可见只有49 = 7*7和161 = 7*23不是素数。
对于n ≤ 10000，一共有2202个t(n)是素数。
对于n ≤ 50,000,000，一共有多少个t(n)是素数？