This article generalizes the concept of prime numbers by defining n-th numbers as natural numbers with exactly n+1 divisors. The author provides the divisor formula based on prime factorization and proves key properties, such as 1 being the only 0-th number, classical primes being 1-th numbers, and squares corresponding to even-indexed n-th numbers.
A fictional retrospective set in 2036 describes the discovery that RSA-2048 had been factored, revealed through a series of mysterious cryptocurrency thefts and subsequent cryptographic failures that led an ISP network administrator to deduce a breakthrough in solving hard mathematical problems, ultimately confirmed when the factors were posted anonymously.
RSA-896 is a RSA cryptographic challenge number that was factored on September 19, 2026 using Claude. The factorization yields two large prime numbers p and q whose product equals the original RSA-896 number.