20091220, 15:45  #1 
Dec 2009
3^{3} Posts 
Somebody made a numerical mistake
C. Caldwell and G. L. Honaker, Jr., Prime Curios! The Dictionary of Prime Number Trivia, CreateSpace, 2009.
On page 160 there's an 'interesting' curio. 27941 The only known prime p such that n^2  n + p produces exactly 600 primes for n = 0 to 1000.[Rodriguez] My program found exactly 599 primes. 
20091220, 16:45  #2 
Jun 2003
1360_{16} Posts 
Post your results.
BTW, the form is (n^2  n + p) 
20091220, 16:55  #3 
"Robert Gerbicz"
Oct 2005
Hungary
1466_{10} Posts 
Code:
? sum(n=0,1000,isprime(n*nn+27941)) %1 = 600 
20091220, 17:08  #4 
Jun 2003
2^{5}×5×31 Posts 
Probably because n=0 & n=1 yields the same prime.

20091220, 17:56  #5 
Dec 2009
3^{3} Posts 

20091220, 18:17  #6 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10253_{8} Posts 

20091220, 19:02  #7 
Dec 2009
3^{3} Posts 
Reduce to absurdity:
0*n^2  0*n + 27941 produces 1001 primes for n = 0 to 1000. Stock tale... 
20091220, 22:12  #8 
Dec 2009
33_{8} Posts 
This thread is a little alarmist.
If we do a list of primes (from the smaller to the largest) we'll see 599 numbers. I think that it should be noted that there is a dupe number. Do you agree with me? Last fiddled with by Arkadiusz on 20091220 at 22:22 
20091220, 22:21  #9  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3×1,571 Posts 
Quote:
Have you found another p which produces exactly 600 primes?


20091221, 03:32  #10 
"William"
May 2003
New Haven
939_{16} Posts 

20091221, 03:53  #11  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22322_{8} Posts 
Quote:
But this polynomial does not produce 600 primes, does it? So it doesn't have anything to do with the OP. Where is the absurd? We can quibble on the definition of "produces"? Does it imply "distinct", "unique"? 

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