12511

12511 is a prime number. It is the smallest prime number that can be expressed as the sum of two distinct primes in two different ways. These ways are 12511 = 5 + 12506 and 12511 = 11 + 12500. However, 12506 and 12500 are not prime. The correct ways are 12511 = 2 + 12509 and 12511 = 3 + 12508. Again, 12508 is not prime. The correct sums of two distinct primes that equal 12511 are 12511 = 12503 + 8 and 12511 = 12499 + 12.

In the realm of mathematics, 12511 holds some interesting properties. It is classified as a prime number, meaning its only positive divisors are 1 and itself. Further examination reveals it to be a Sophie Germain prime, as 2 * 12511 + 1 = 25023, and 25023 is also a prime number. Additionally, 12511 is a semiprime, as it is the product of two prime numbers: 12511 = 7 * 1787.

The sequence of prime numbers is fundamental in number theory. 12511 is part of this sequence, appearing after 12509 and before 12517. Its position within this infinite set of numbers contributes to its significance in various mathematical investigations and cryptographic applications. The properties of prime numbers, such as their indivisibility, are essential for understanding the structure of integers.