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Old 2009-12-20, 15:45   #1
Arkadiusz
 
Dec 2009

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Question 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.
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Old 2009-12-20, 16:45   #2
axn
 
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Post your results.

BTW, the form is (n^2 - n + p)
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Old 2009-12-20, 16:55   #3
R. Gerbicz
 
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"Robert Gerbicz"
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Code:
? sum(n=0,1000,isprime(n*n-n+27941))
%1 = 600
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Old 2009-12-20, 17:08   #4
axn
 
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Probably because n=0 & n=1 yields the same prime.
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Old 2009-12-20, 17:56   #5
Arkadiusz
 
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Quote:
Originally Posted by axn View Post
Probably because n=0 & n=1 yields the same prime.
Produced primes:
27941, 27943, ... , 1026941.

I still see 599 numbers.
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Old 2009-12-20, 18:17   #6
Mini-Geek
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"Tim Sorbera"
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Quote:
Originally Posted by Arkadiusz View Post
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.
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Old 2009-12-20, 19:02   #7
Arkadiusz
 
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Reduce to absurdity:

0*n^2 - 0*n + 27941 produces 1001 primes for n = 0 to 1000.

Stock tale...
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Old 2009-12-20, 22:12   #8
Arkadiusz
 
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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
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Old 2009-12-20, 22:21   #9
Batalov
 
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Quote:
27941
The 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?
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Old 2009-12-21, 03:32   #10
wblipp
 
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Quote:
Originally Posted by Batalov View Post
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.
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Old 2009-12-21, 03:53   #11
Batalov
 
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Quote:
Originally Posted by Arkadiusz View Post
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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