They are called twin primes and there are thought to be infinitely many such pairs.
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2 and 5 are the only prime numbers which differ by 3.
1 and 2
If you mean consecutive numbers that are prime? than the answer is 2,3 are consecutive numbers which are prime. except for this pair it is impossible for consecutive numbers to be prime because every second number is multiple of 2
2 and 3 is the only pair.
The last known twin prime number as of now is 2996863034895, which is part of the twin prime pair (2996863034895, 2996863034897). Twin prime numbers are prime numbers that differ by 2. However, it is worth noting that there may be larger twin prime numbers that have not been discovered yet.