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(just those submitted by Bergot)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

Just showing those entries submitted by 'Bergot': (Click here to show all)

+ Take the nine pairs (a,b) with a+b=19; take the sum a*b+19 for all these nine pairs; ALL the sums are primes. 19 is the largest prime that will do this. [Bergot]

+ Using the first three primes to get complex numbers 2+3*i and 3+5*i, multiply them to get the third number -9+19*i to be used as the three points (2,3), (3,5), and (-9,19) creating a triangle, which will have an area of 19, the same as the last y-value. [Bergot]

+ Consider i + j = 19 for 0 < i, j < 19 and i * j + 19 is prime for ALL cases: 1*18+19=37, 2*17+19=53, 3*16+19=67, 4*15+19=79, 5*14+19=89, 6*13+19=97, 7*12+19=103, 8*11+19=107, 9*10+19=109. This also works for 2 and 7. Can it work for a prime greater than 19? [Bergot]

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