A290507 Sums and differences of products of the first n primes partitioned into two disjoint parts.

1, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 47, 67, 73, 83, 89, 97, 101, 103, 107, 127, 131, 139, 151, 157, 163, 169, 179, 181, 199, 221, 227, 239, 241, 263, 307, 313, 323, 337, 347, 349, 353, 359, 361, 379, 383, 389, 391, 397, 421, 457, 463, 467, 491, 499, 521, 527, 601, 619, 643, 653, 667, 673, 709, 713

Offset: 1

Author

Yves Debeuret, Aug 04 2017

Keywords

• nonn

Comments

Partition the set Pn = {2,3,5,...,pn} of the first n primes into two disjoint parts. Let a,b be their respective products, S = a + b and D = |a - b|. The list is composed of sorted values of S and D.

Numbers a,b share no common factors. It follows that the prime factors of S or D can't divide either a or b. So the smallest possible prime factor of S or D is pn+1.

After the value 1, the next 25 numbers of the list are primes. Then the proportion of primes decreases. For the first 2000 elements, about 50% are primes.

Examples

			3 - 2 = 1
2 + 3 = 5
2*5 - 3 = 7
2*3 + 5 = 11
2*5 + 3 = 13
3*5 + 2 = 17
2*3*5 - 7 = 23
2*7 + 3*5 = 29
2*5 + 3*7 = 31
...
		

Links

• C. Aebi and G. Cairns, Partitions of Primes, Parabola, Vol. 45, No. 1 (2009).

Programs

JavaScript