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

Question

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

bibby · Answer

What class is this for?

bibby · Answer

you can use the miller rabin primality test I think

bibby · Answer

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

bibby · Answer

$3^{2106} \cancel{\equiv} 1 \mod 2107$

unklerhaukus · Answer

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?

rational · Answer

21 is divisible by 7
and 07 is divisible by 7

so we can eyeball that the next prime is a divisor of 2107

unklerhaukus · Answer

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