The largest integer n with the property that every smaller integer relatively prime to n is itself a prime.
3030 + 1 - 30 + 1 is prime. [Luhn]
n is a Giuga number if p divides (n/p-1) for every prime divisor p of n. 30 is the smallest such number.
30*2^30-1 is a Woodall prime. [Dobb]
30 is the largest two-digit number such that 30^30+30-1 is prime. [Opao]
The product of first five nonzero Fibonacci numbers. Note that 30 + 1 and 30 - 1 are twin primes. [Gupta]
Zhi-Wei 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]
(There is one curio for this number that has not yet been approved by an editor.) To link to this page use http://primes.utm.edu/curios/page.php?number_id=45
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