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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest integer n with the property that every smaller integer relatively prime to n is itself a prime. 30^{30 + 1}  30 + 1 is prime. [Luhn] n is a Giuga number if p divides (n/p1) for every prime divisor p of n. 30 is the smallest such number. 30*2^301 is a Woodall prime. [Dobb] 30 is the largest twodigit number such that 30^30+301 is prime. [Opao] The product of first five nonzero Fibonacci numbers. Note that 30 + 1 and 30  1 are twin primes. [Gupta] ZhiWei SUN conjectured in May 2008 that exactly 30 odd integers > 1, all multiples of 3, cannot be written in the form p + n(n+1), where p is a prime congruent to 1 (mod 4) and n a natural number. It is twice more than when p is congruent to 3 (mod 4). [Capelle] Least integer the sum of whose distinct semiprime factors is prime. Semiprimes (6, 10, 15) divide 30, and 6 + 10 + 15 = 31. [Post] The smallest sphenic number whose prime factors form a primedigit prime, i.e., 523. [Loungrides] The smallest sphenic number, 2*3*5, that can also be represented as sum of two consecutive emirps, i.e., 13+17, is also an oblong number, i.e., 5*6. [Loungrides]
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