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 2009-12-20, 15:45 #1 Arkadiusz   Dec 2009 33 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. 27941The 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.
 2009-12-20, 16:45 #2 axn     Jun 2003 136016 Posts Post your results. BTW, the form is (n^2 - n + p)
 2009-12-20, 16:55 #3 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 146610 Posts Code: ? sum(n=0,1000,isprime(n*n-n+27941)) %1 = 600
 2009-12-20, 17:08 #4 axn     Jun 2003 25×5×31 Posts Probably because n=0 & n=1 yields the same prime.
2009-12-20, 17:56   #5

Dec 2009

33 Posts

Quote:
 Originally Posted by axn Probably because n=0 & n=1 yields the same prime.
Produced primes:
27941, 27943, ... , 1026941.

I still see 599 numbers.

2009-12-20, 18:17   #6
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

102538 Posts

Quote:
 Originally Posted by Arkadiusz Produced primes: 27941, 27943, ... , 1026941. I still see 599 numbers.
For n=0 through n=1000, 600 n's produce primes. n=0 and n=1 produce the same prime, which is the same as p: 27941. There are 599 unique prime among the 600.

 2009-12-20, 19:02 #7 Arkadiusz   Dec 2009 33 Posts Reduce to absurdity: 0*n^2 - 0*n + 27941 produces 1001 primes for n = 0 to 1000. Stock tale...
 2009-12-20, 22:12 #8 Arkadiusz   Dec 2009 338 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 2009-12-20 at 22:22
2009-12-20, 22:21   #9
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×3×1,571 Posts

Quote:
 27941The only known prime p such that n^2 - n + p produces exactly 600 primes for n = 0 to 1000. /Rodriguez/
This 'curio' is correct. You are quibbling about the definition, but this is beside the point.

Have you found another p which produces exactly 600 primes?

2009-12-21, 03:32   #10
wblipp

"William"
May 2003
New Haven

93916 Posts

Quote:
 Originally Posted by Batalov This 'curio' is correct.
No, the curio is wrong. It should say:

The only known prime p such that n^2 - n + p produces primes exactly 600 times for n = 0 to 1000.

2009-12-21, 03:53   #11
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

223228 Posts

Quote:
 Originally Posted by Arkadiusz Reduce to absurdity: 0*n^2 - 0*n + 27941 produces 1001 primes for n = 0 to 1000.
This statement is also true.
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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