OFFSET
1,1
COMMENTS
These "proximate-prime polynomials" exhibit high prime densities. Of the 333 under 100000, 46 have greater than 50% prime values for the first 1000 terms. 2221 positive-only PPPs have been found under 1000000. All positive-integer PPPs have complex roots (only negative-integer PPPs, which are excluded) have real roots. The roots mostly have a real part of 1/2 or a multiple of 1/2.
REFERENCES
Purple Math: Finding the Next Number in a Sequence: The Method of Common Differences http://www.purplemath.com/modules/nextnumb.htm
Robert Sacks, Method of Common Differences http://www.numberspiral.com/p/common_diff.html
LINKS
Michael M. Ross The High Primality of Prime-Derived Quadratic Sequences (2007)
Michael M. Ross How to Use Qtest (2007)
FORMULA
Method of common differences: if (P2 - P1) - (P3 - P2) = (P3 - P2) - (P4 - P3) then polynomial is degree 2.
EXAMPLE
For 17, 19, 23, 29 the method of common differences produces coefficients of 1, -1 and 17 for a polynomial expression of n^2 - n + 17.
CROSSREFS
KEYWORD
nonn,uned,tabf
AUTHOR
Michael M. Ross, Jul 24 2008
STATUS
approved