Question

[Nguyễn Hồng Anh]

how many different prime numbers a's are there such that a+20 and a+40 are also prime numbers

Answer 1

[Đoàn Đức Hà]

If \(a=2\): \(a+20=22\)is not a prime number. 

If \(a=3\): \(a+20=23\), \(a+40=43\)are both prime numbers. 

If \(a>3\), we have \(a=3k+1\)or \(a=3k+2\).

- \(a=3k+1\Rightarrow a+20=3k+21⋮3\)is not a prime number. 

- \(a=3k+2\Rightarrow a+40=3k+42⋮3\)is not a prime number.