73
This number is a prime.
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The smallest prime that divides a 7-digit number of the
form p0p, where p is any 3-digit
prime. [Beedassy]
The largest known prime that starts a chain (generated by
the quadratic 73 - x - x2, for
x = 0, 1, 2, ... , 7) of smaller, increasingly
distant primes with successive gap 2n, (n =
1, 2, 3, ..., 7): 73, 71, 67, 61, 53, 43, 31, 17. [Beedassy]
The smallest prime with prime digits that belongs both to
an emirp pair (37, 73) and to a twin prime pair (71, 73) as
the larger member. [Beedassy]
The smallest prime that is the middle term of three
consecutive numbers each expressible as a sum of two
nonzero squares: 72 = 62 + 62 ; 73 =
32 + 82 ; 74 = 52 +
72. Note that replacing the first prime digit 7
by the prime 23 forms instead the smallest prime (233) that
is the middle term of three consecutive numbers each
expressible as a sum of two distinct nonzero
squares: 232 = 62 + 142 ; 233 =
82 + 132 ; 234 = 32 +
152. [Beedassy]
73 is the only
Sheldon prime, i.e., i) whose binary representation is
palindromic (10010012) and ii) which belongs to
an emirp pair (Pn, Pm)
such that subscripts (m, n) = (21, 12) are
also reversals of each other and n has a prime
decomposition 21 = 3*7 that concatenates back to
Pm (Carl Pomerance, Chris Spicer,
February 2019). [Beedassy]