Are there any prime numbers in the pascal's triangle?

Question

I mean except the two second diagonals by the side of the Pascal's Triangle which consists of consecutive numbers.

If yes, can you say what it is and where does it appear in the Pascals' Triangle?

If no, can you pls proove it?

4 is not a prime!! its 2x2!!

Answer 1

The numbers in Pascal's Triangle are the binomial coefficients. They are all of the form nCk = n!/k!(n-k)!
nC0 = nCn = 1
nC1 = nC(n-1) = n

For other values of k, the terms in nCk cannot cancel to leave a single prime factor.
Why?
For 1 < k, n < nCk, if nCk is prime it has to be a prime larger than n, but it is the product of terms that are all less than n, so that can't be the case.

Answer 2

No, there are not any.

Here is why.

If it is even, it is not prime.

If it is odd, then it is divisible by an element within the prime factorization of the value next to it nearest its 1 diagonal.

So the only prime numbers occur on the 2nd diagonal.

Q.E.D.

Answer 3

thuier are millions.eg:1,3,5,7............