Question

Is 2107 a prime number? What is its prime factorization?

Answer 1

What class is this for?

Answer 2

you can use the miller rabin primality test I think

Answer 3

also http://en.wikipedia.org/wiki/Fermat%27s_little_theorem

Answer 4

\(3^{2106} \cancel{\equiv} 1 \mod 2107\)

Answer 5

2107 is not divisible by 2,
last digit is not {0,2,4,6,8}

2107 is not divisible by 3,
because 3x700 = 2100, 3x701=2103, 3x702= 2106, 3x703=2109

2107 is not divisible by 5 because the last digit is not {0,5}

is 2107 divisible by the next prime number?

Answer 6

21 is divisible by 7
and 07 is divisible by 7

so we can eyeball that the next prime is a divisor of 2107

Answer 7

7x300 = 2100,
7x ??? = 2107

is ??? prime?