OFFSET
1,1
LINKS
Michael M. Ross, What Are Odd Squared, or Biquadratic, Paired Primes?
Michael M. Ross, Diagram of paired primes showing how two perfect pairs partially overlap: 23 and 43 span perfect squares 25 and 36; 29 and 53 span perfect squares 36 and 49.
Michael M. Ross, VBA source code providing an Excel visualization of the odd-offset prime pairs and colocation with twin primes.
FORMULA
PS1 + OfN = P1, PS3 + OfN = P2, where
PS1 = first perfect square,
PS3 = 3rd perfect square,
OfN = an equal positive offset from preceding perfect square, and
P1 and P2 = the prime pair.
EXAMPLE
Prime pair 71 and 107 have an odd offset of 7 from 64 and 100:
Interval 1: 8*8 = 64 + 7 = 71.
Interval 2: 9*9 = 81 + 7 = 88.
Interval 3: 10*10 = 100 + 7 = 107.
Prime pair 97 and 137 have an even offset of 16 from 81 and 121:
Interval 1: 9*9 = 81 + 16 = 97.
Interval 2: 10*10 = 100 + 16 = 116.
Interval 3: 11*11 = 121 + 16 = 137.
In all cases there is a complete intermediate quadratic interval (#2).
The pair (11,83), 11-9 = 83-81 = 2, does not work because there are 6 squares in between: 16,25,36,49,64,81.
PROG
Excel VBA available at http://www.naturalnumbers.org/quadprimes.html#code Demonstrates odd-offset prime-pair distribution with associated twin primes. Limitations: -Only the subset of paired primes for even perfect squares with odd offsets are demonstrated. -Because of the 256-column limitation for an Excel worksheet, data in rows after perfect square 484 are not complete. -Only twin primes that are also paired primes are outlined (in red).
CROSSREFS
KEYWORD
nonn,tabf,more,less
AUTHOR
Michael M. Ross, Feb 04 2008
STATUS
approved