Super-Poulet number

A super - Euler pseudoprime is a Euler pseudoprime to the base a, all of whose divider exclusively from the 1, primes, other Eulerian pseudo- primes of the same base a and is even. Equivalent is the definition: Super - Eulerian prime number is called a composite number, if these two factors are provided for each decomposition into two factors m1 and m2 equations. Super - Euler pseudo- prime to base 2 is also called super- Poulet numbers.

Properties

All factors of a super - Euler pseudoprime, including 1 and the super Euler pseudoprime have the following property:

Example

294409 is a super Euler pseudoprime to base 2 Your dividers are 1, 37, 73, 109, 2701, 4033, 7957 and 294,409th

37, 73 and 109 are prime numbers, 2701, 4033 and 7957 are even super- Euler pseudo- prime to the base.

Super - Eulerian pseudo primes with 3 or more prime factors

It is relatively easy to construct a super - Euler pseudoprime to the base a with three prime factors. You have to find three Euler pseudo- prime to the base a that hold together three common prime factors. The product of these three prime numbers is in turn an Euler pseudo-prime, and thus a super- Euler prime.

Super - Poulet numbers with up to 7 prime factors you can get from the following four quantities:

They come from Gerard Michon

So 1,118,863,200,025,063,181,061,994,266,818,401 = 6421 * 12841 * 51361 * 57781 * 115561 * 192601 * 205441 a super - Poulet number with seven prime factors whose divisor of prime numbers, Poulet numbers and super - Poulet - numbers there (there are a total of 120 chicken - numbers).

Stripped Super - Poulet numbers

When not using the condition that the divisors of Super - Poulet numbers other Poulet numbers than the super - Poulet number must include yourself, you can also expect the chicken numbers to have only two prime factors.

The smallest thus stripped-down super- Poulet number is the 341 with the prime divisors 11 and 31