What is a permutable prime number?

A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits’ positions switched through any permutation and still be a prime number. H. E. Therefore, the base 2 permutable primes are the Mersenne primes.

Is 1111111111111111111 a prime?

If only a single digit is used, only 1s can give a prime: 11, 1111111111111111111 and 11111111111111111111111 are prime with 2, 19 and 23 repetitions of the digit 1. Primes also result from 1 repeated 317 or 1031 times.

What is absolute prime numbers?

A natural number is said to be an absolute prime if it is prime and. remains prime after any permutation of its digits. Prove that the. decimal representation of an absolute prime number can contain. no more than three distinct digits.

What is composed of prime numbers?

Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.

Which is the correct definition of a permutable prime?

Permutable prime. Any repunit prime is a permutable prime with the above definition, but some definitions require at least two distinct digits. All permutable primes of two or more digits are composed from the digits 1, 3, 7, 9, because no prime number except 2 is even, and no prime number besides 5 is divisible by 5.

Are there any permutable primes in base 2?

In base 2, only repunits can be permutable primes, because any 0 permuted to the ones place results in an even number. Therefore, the base 2 permutable primes are the Mersenne primes.

Is the OEIS index a permutable prime number?

OEIS index. A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits’ positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to study these primes, called them permutable primes, but later they were also called absolute primes.

Who was the first to study permutable primes?

H. E. Richert, who is supposedly the first to study these primes, called them permutable primes, but later they were also called absolute primes. In base 10, all the permutable primes with fewer than 49,081 digits are known