19

This number is a prime.

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]

+ 19 squared can be written as the sum of three consecutive squared triangular numbers (6^2 + 10^2 + 15^2). [Bergot]

(There is one curio for this number that has not yet been approved by an editor.)

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell