30103
(another Prime Pages' Curiosity)
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+ The only known multidigit palindromic prime found by averaging the divisors of a composite number. [McCranie and Honaker]

+ The sum of 37 consecutive primes (30103 = 683 + 691 + 701 + ... + 937 + 941). [Rivera]

+ Solution to the quadratic equation n2 + n + 1 when n is substituted with prime 173. [De Geest]

+ The decimal expansion of the common logarithm of two rounded to five digits. [La Haye]

+ The sum of three consecutive palindromic primes starting with 30103 is a palindromic prime as well (30103 + 30203 + 30403 = 90709). [De Geest]

+ The smallest palindromic prime such that another (370717073) emerges after intertwining it with the digital sum of itself. [De Geest]

+ The smallest palindromic prime yielded by a prime (173) of the form p^2+(p+1). [Silva]

+ 2^2+p^2+q^2+r^2 = N with p < q < r are all prime in ten different ways: (7,59,163), (11,73,157) (A), (13,103,139), (13,113,131) (A), (19,43,167), (29,37,167), (37,97,139), (41,43,163) (B), (53,67,151), (89,97,113). Note that (a) N is J. McCranie / G. L. Honaker Jr.'s palindromic prime from July 1998 with a recent 2009 supplement from A. Vrba, (b) the smallest prime base item has to be 2^2, (c) two representations (A) with two emirps and a palindromic prime, in (B) p and q are prime twins and R(163)=19^2! [Krug]




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