2867200

2867200 is a number that appears in various mathematical, astronomical, and computational contexts, often due to its significance in specific fields or algorithms. It is most notably recognized as a key value in the **Sierpiński triangle** and **Mersenne prime** searches, particularly in the context of the **Sierpiński problem** and **Lucas-Lehmer primality test**.

In number theory, 2867200 is the exponent used in the **Lucas-Lehmer test** to determine whether a Mersenne number of the form 2^p − 1 is prime. This test is applied to Mersenne exponents that are part of the **Sierpiński problem**, which seeks to identify odd integers *k* for which all numbers of the form *k*·2^n + 1 are composite. The number 2867200 is one such exponent where the Lucas-Lehmer test was historically relevant in verifying primality.

Additionally, 2867200 has appeared in computational mathematics as part of large-scale factorization challenges or pseudorandom number generation algorithms. Its inclusion in certain mathematical proofs or conjectures stems from its role in iterative processes, such as those used in the **AKS primality test** or other number-theoretic computations.

While not inherently meaningful in everyday contexts, its appearance in advanced mathematical research underscores its utility in theoretical explorations of prime numbers and computational efficiency. The number itself does not hold a specific real-world application but serves as a critical component in specialized mathematical frameworks.