P. Goetgheluck, On cubic polynomials giving many primes, Elem. Math. 44 (1989), 70-73.  Home/Search   Document Not in Database   Summary   Related Articles

....the challenge at the end of their paper of nding quadratic polynomials which generate 100 primes in the interval [0; 99] Karst [K1] de ned high density to be at least 60 in the interval [0; 159] and found several such polynomials of the form x 2 x A, where A is negative. Goetgheluck [Goe], in studying cubic polynomials, set the bar at 75 in the interval [0; 99] Fung and Williams [Fu] consider the density of polynomials f p (x) x 2 x p and show that f 27941 (x) and f 41 (x) produce, respectively, 286128 and 261080 primes in the interval [0; 1000000] Here we see a ....

....(that is, prime or unit) because f 1 ( 3) 1, f 2 (3) 1 and f 3 (13) 1 . Actually f 1 (x) is prime for all integers in the interval [ 2; 10] and f 2 (x) is prime for all integers in the interval [4; 14] On page 203 of [Ri2] Ribenboim lists two cubic polynomials discovered by Goetgheluck [Goe]: x 3 34x 2 381x 1511 and 2x 3 45x 2 331x 3191 that assume prime values at 0; 1; 25. Goetgheluck lists a table of 21 cubic polynomials that produce at least 75 primes in the interval [0; 99] The above two polynomials were obtained from (14) and (15) in his table by ....

P. Goetgheluck, On cubic polynomials giving many primes, Elem. Math. 44 (1989), 70-73.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC