Lemoine’s Conjecture or Levy’s Conjecture

Lemoine’s conjecture or Levy’s conjecture, named after Emile Lemoine and Hyman Levy, respectively, is a popular conjecture as far as the number theory is concerned.

According to this conjecture, every odd positive integer greater than 5 can be expressed as the sum of an odd prime number and an even semiprime.

A prime number other than 2 is called an odd prime number.

A semiprime is the product of two prime numbers.

As per the definition, every odd positive integer n > 5 is the sum of an odd prime p and an even semiprime 2q.

Mathematically, n = sum(p + (2q)).

Conditions

Condition 1: Integer n must be odd.

Condition 2: Integer n must be greater than 5.

For Example

Integer n: 7

Sum of an odd prime p and even semiprime 2q: 3 + (2 x 2) => 7.

Integer n: 11

Sum of an odd prime p and even semiprime 2q: 5 + (2 x 3) => 11.

Integer n: 13

Sum of an odd prime p and even semiprime 2q: 7 + (2 x 3) => 13.

Integer n: 17

Sum of an odd prime p and even semiprime 2q: 7 + (2 x 5) => 17.

Integer n: 47

Sum of an odd prime p and even semiprime 2q: 13 + (2 x 17) => 47.

Hope you have understood this amazing concept of Lemoine’s conjecture or Levy’s conjecture.