Try this beautiful problem from Integer based on Prime number useful for ISI BStat Entrance.
The number of integers \(n>1\), such that n, n+2, n+4 are all prime numbers is ......
But try the problem first...
TOMATO, Problem 70
Challenges and Thrills in Pre College Mathematics
taking n=3, 5, 7, 11, 13, 17....prime numbers we will get
Case of n=3
Case of n=5
n+4=9 which is not prime....
Case of n=7,
n+2=9 which is not prime ...
Can you now finish the problem ..........
We observe that when n=3 then n,n+2,n+4 gives the prime numbers.....other cases all are not prime.Therefore any no can be expressed in anyone of the form 3k, 3k+1 and 3k+2.
can you finish the problem........
If n is divisible by 3 , we are done. If the remainder after the division by 3 is 1, the number n+2 is divisible by 3. If the remainder is 2, the number n+4 is divisible by 3
The three numbers must be primes! The only case n=3 and gives\((3,5,7)\)
From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here: