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C. J. Mozzochi utilized 1051 to show that if we let p(n)
be the nth prime, then there exists a constant K such that
p(n+1)  p(n) is less than K p(n)^(1051/1920). [Post]
1051 = (1*1051) + (0*1051) + (5*1051) + (1*1051). [Aghasoltan] The largest known number n such that there is no prime between n^{k} and (n+1)^{k}, where k = 3/2. [Capelle] The sum of all odd semiprimes less than a hundred. [Silva] A book known as "The Great Omar" sank with the Titanic and has not been recovered. It contained 1051 precious and semiprecious stones set in eighteencarat gold. There are at least 1051 cases in which the nth Honaker prime has the same number of digits as the nth square. The smallest are 4397 and 1024 (32^2). The largest known are 1066157 and 9998244 (3162^2). Could there possibly be more? [Gaydos]
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