The book is now available! 1331
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ A prime number cubed (11) that is a cube in every base (in base 4, 1331=64+48+12+1 in base 10=125=5 cubed, in base 5, 1331=125+75+15+1=216=6 cubed, in base 6 it is 7 cubed, in base 7 it is 8 cubed, etc. This is because it is row 3 of Pascal's triangle (in which every row is a power of 11) and therefore in every base that holds it. It's value in that base showed in base ten is equivilent to the original base number plus 1 cubed. In a formula, 1331(base b)=(b+1)^3. [DeMio and Hudgins]

+ The sum of three consecutive primes {439, 443 and 449}. It is the smallest cube of this form. [Bajpai]

+ 1331- 12*n - 12*n^2 is prime for n = 1 to 10. Note that the expression is equal to 11^3 for n = 0 and to 11 for n = 10. [Petrov]

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