17251795

The number **17251795** is primarily notable as a significant figure in the context of cryptography and computational mathematics, particularly in relation to the RSA encryption algorithm. RSA is a widely used public-key cryptosystem that relies on the difficulty of factoring large composite numbers into their prime factors. The number 17251795 is the product of two large prime numbers, 11457 and 15107, which were used in early demonstrations of RSA encryption to illustrate the security of the algorithm.

In 1977, Ron Rivest, Adi Shamir, and Leonard Adleman, the inventors of RSA, published a paper introducing the method. They included the factorization of 17251795 as an example to show how RSA could be implemented. The number was chosen because it was large enough to be computationally challenging to factor at the time, yet small enough to be manageable for illustrative purposes. This example helped demonstrate the practicality of RSA while highlighting the computational difficulty of breaking the encryption if the prime factors were unknown.

While 17251795 itself is not widely referenced in modern cryptographic applications due to its small size, its historical significance lies in its role in the early development of RSA. Today, RSA systems use much larger numbers—often hundreds or thousands of digits long—to ensure security against factoring attacks. The study of 17251795 remains relevant in educational contexts as a foundational example of how RSA encryption works and why large primes are essential for secure communication.