Primes

Question 1

not prime

Answer 1

composite

Question 2

prove there are infinitely many primes

Answer 2

Q = p1p2…pn + 1

Question 3

Mersenne Prime

Answer 3

2^p - 1

Question 4

The prime number theorem

Answer 4

lim as x-> infinity pi(x)/(x/ln(x)) = 1

Question 5

What does the prime number theorem say about the odds of a number being prime

Answer 5

1/ln(n)

Question 6

All primes greater than 2 are;

Answer 6

odd

Question 7

For every positive integer n there is an arithmetic progression of length n consisting of

Answer 7

entirely primes

Question 8

two integers m and n are relatively prime if

Answer 8

gcd(m,n) = 1

Question 9

gcd(a,b) * lcm(a,b) =

Answer 9

a*b

Question 10

The multiplicative inverse of n mod(m) exists iff

Answer 10

m and n are relatively prime

Question 11

You should check out a proof of the uniqueness of the prime facorization of a positive integer

Answer 11

do it

Question 12

The chinese remainder theorem

if

x = i mod m

x = j mod n

x = k mod o

and m n o are pairwise relatively prime

then

Answer 12

x = inn’oo’ + jmm’oo’ + kmm’oo’

Question 13

Fermat’s little theorem

if p is prime and a is not divisible by p then

Answer 13

a^(p-1) = 1 mod p

Question 14

what is 7^222 mod 11

Answer 14

5

Question 15

when is m pseudoprime mod n

Answer 15

m^(n-1) = 1 (mod n)

Question 16

a primitive roor modulo p is an integer r in Zp such

Answer 16

that every nonzero element of Zp is a power of r

Question 17

log 5 mod 11 base 2

Answer 17

4