mostly on computers and mathematics
2^512 + 75 - 1 = 48464351211032890093 * n
2^512 - 569 - 1 is harder.
2^384 - 317 -1 = 2633349255961 * 242009720353150597 * n
What is the prime p nearest to 2^1024 such that p-1 is factored?
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