|

Algebra

New kid on the Block

 Joined: 15 Jan 2008 Post: 8
19 Jan 2008 08:39:45 IST
0 People liked this
4
653
ppl prove this
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

there does not exist any largest prime no

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
19 Jan 2008 08:44:57 IST
2 people liked this

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))

New kid on the Block

Joined: 12 Jan 2008
Posts: 13
19 Jan 2008 18:38:21 IST
0 people liked this

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

Blazing goIITian

Joined: 17 Jan 2008
Posts: 510
21 Jan 2008 15:33:55 IST
1 people liked this

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

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
21 Jan 2008 16:22:59 IST
0 people liked this

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
232,582,657-1 (discovered in sept, 06, as far as i remember)

that means 232,582,657-1 is the largest prime number known of (2 power any prime number) -1 type.

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.

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 9960 m Post - 2185
4. edison
 Altitude - 10815 m Post - 7797
5. Sagar Saxena
 Altitude - 8625 m Post - 8064
 Altitude - 6330 m Post - 1979

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone