Which of the following is a counter-example to the statement "For all positive integers n, (2n) + 1 is a prime

Question

Which of the following is a counter-example to the statement "For all positive integers n, (2n) + 1 is a prime number"?


1. n=1
2. n=2
3. n=3
4. n=4

Answer 1

n=4 is a counter-example because 2(4)+1 = 9, which is not a prime.

Answer 2

4. n=4, 2 x 4 = 8 + 1 = 9, 9 is not a prime number.

Answer 3

n=4, 2(n)+1=9

Answer 4

1. n = 1, 2n + 1 = 3, 3 is prime
2. n = 2, 2n + 1 = 5, 5 is prime
3. n = 3, 2n + 1 = 7, 7 is prime
4. n = 4, 2n + 1 = 9, 9 is NOT prime

Answer 5

4 since 9 is not a prime number

Answer 6

4. n=4 (since this gives the result 9 when using 2n + 1, which is not a prime no. n=1,2,3 gives the answers 3,5,7 (respectively), all of which are prime no's)

Answer 7

n=4, since 2*4+1 = 9 = 3^2, which is not prime.
The other choices give 3,5,7 which are all prime.

Answer 8

Not quite, If I understand you correctly. Assume that p1, p2, ........., pn are the only primes where p1 < p2 < .... < pn Suppose Q = p1 * p2 * ..... * pn +1 Since none of the pk (1<= i <= n) can divide Q (pk divides Q - 1 => pk cannot divide Q), we conclude that either Q is a prime greater than pn or Q is a composite integer divisible by a prime greater than pn Either conclusion implies that the original assumption that there are a finite number of primes is false

Answer 9

By trying each case, you see that of the list of (2n+1):

1. 3
2. 5
3. 7
4. 9,

9 is not prime.

Answer 10

4 Silly