The numbers 13 and 31 are indeed both prime numbers and share the same digits, which makes them a fascinating pair. To find other such pairs of prime numbers up to 100, we need to identify all prime numbers in this range first.
Prime numbers are defined as numbers greater than 1 that have no positive divisors other than 1 and themselves. So, let’s list the prime numbers up to 100:
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23
- 29
- 31
- 37
- 41
- 43
- 47
- 53
- 59
- 61
- 67
- 71
- 73
- 79
- 83
- 89
- 97
Now, we check for pairs of these primes that consist of the same digits:
- (13, 31)
- (17, 71)
- (37, 73)
These pairs show that prime numbers can indeed share the same digits, even when their values differ significantly. Each pair can be reversed to form another prime, illustrating a delightful coincidence in number theory.