Beauty of Numbers Ep - 3 | Series on Number Theory | Prime Numbers | Cheenta | Rajdeep

[@AtifAhad-i2n]

Hi. Vaiya❤❤❤❤❤

[@abhinavkumarverma2224]

(i) 4k-1 means the form 4k+3. We can see that 4k is divisible by 2 and k and 4k+2 is also divisible by 2 for k>0. Therefore, all the primes are of the form 4k+1 and 4k-1 (ii)Let us assume that there are finite number of prime numbers p1,p2,p3,... of the form 4k-1 Let N = 4×p1×p2×p3×... - 1 We can see that no p1,p2,p3... can divide N. Hence it is a new prime. Here we get a contradiction. Therefore we can say that there are infinitely many prime numbers of form 4k-1