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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest known difference between consecutive Ulam numbers (332250401 and 332251032). [Knuth] 631 values of n < 1000 produce primes for 2n^{2} + 144251. Note that 631 is prime also. [McLean] The reverse concatenation of the first three triangular numbers. [Gupta] The tetractys (pronounced "tettrak'tis") is a triangular figure consisting of ten vertices arranged in four rows: one, two, three, and four dots in each row. It was a mystical symbol to the Pythagoreans, who lived during the 6th century B.C. There are fifteen primes in the figure below (reading forwards or backwards along the indicated lines), the largest of which is 631. Can you rearrange these digits and achieve two dozen primes?(0) / \ (1)(2) / \ / \ (3)(4)(5) / \ / \ / \ (6)(7)(8)(9) The largest in the fist case of five consecutive primes of form 5^n+6 for n= 0, 1, 2, 3, 4. The sequence of these primes is: 7, 11, 31, 131, 631. [Loungrides] The reversal of the sum of squares of two consecutive triangular numbers (T_{3} and T_{4}). The smallest prime of this form. [Bajpai]
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