IIT JEE , AIEEE Forum - Mathematics , Algebra

kap.mehra

there does not exist any largest prime no

sprinkle

Let the largest prime number is n.

=> 2, 3, 5 .......... n must be the list of ALL prime numbers. any number not in the list is not prime, n is the largest no. in the list.

=> (2*3*5*.......*n + 1) is not divisible by any number (except 1 and itself)

=> (2*3*5*.......*n + 1) is also a prime number

but (2*3*5*.......*n + 1) > n => contradiction (we assumed n is the largest prime)

=> there is no largest prime number DONE!

(remember that if a number is not prime <=> number is divisible by some prime number(s))

sizzle_through

wow i never knew these kind of things can be proved also

sboosy

2 power any prime number -1 always equal to a bigger prime number.

example:

2 cube is 8

8-1=7 which is prime

2 power 5 is 32

32-1=31 which is prime

the rest is there to see

sprinkle

sboosy!

(2 power any prime number) -1 gives one group of prime numbers. e.g. 3, 7, 31 etc.

However, there is another group of prime numbers too which can't be obtained by (2 power any prime number) -1. e.g. 13, 19 etc.

But if u want to prove that there is no largest prime number by using (2 power any prime number) -1 form, you are, sorry to say that, wrong.

As in that case largest prime number is 2^32,582,657-1 (discovered in sept, 06, as far as i remember)

that means 2^32,582,657-1 is the largest prime number known of (2 power any prime number) -1 type.

Please see internet to confirm.

Correct me IF i m somewhere wrong. I may be wrong as this topic is very very controversial among mathematicians. Who knows u will find a bigger prime number than the existing one and will be the next Ramanujan :)

But Yes, there is no largest prime number and that is possible becoz they may not be of (2 power any prime number) -1 type.

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