By:Leyendekkers, JV (Leyendekkers, J. V.)[ 1 ] ; Shannon, AG (Shannon, A. G.)[ 2,3 ]
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Document Type:Article
The row structures of the prime-subscripted Fibonacci numbers in the modular ring Z(4) show distinction between primes and composites. The class structure of the Fibonacci numbers suggest that these row structures must survive to infinity and hence that Fibonacci primes must too. The functions F-p = K-p +/- 1 and Fp (factors) = k(p) +/- 1 support the structural evidence. The graph of (K/k) versus p displays a Raman-spectra form persisting to infinity: ln(K/k) is linear in p in the composite case while primes lie along the p-axis to infinity.
Author Keywords:Fibonacci numbers; Prime numbers; Composite numbers; Modular rings; Raman spectra
Reprint Address: Leyendekkers, JV (reprint author)
Univ Sydney, Fac Sci, Sydney, NSW 2006, Australia. |
Addresses:
[ 1 ] Univ Sydney, Fac Sci, Sydney, NSW 2006, Australia | |
[ 2 ] Univ Technol Sydney, Fac Engn & IT, Sydney, NSW 2007, Australia | |
[ 3 ] Campion Coll, Toongabbie East, NSW 2146, Australia |
E-mail Addresses:t.shannon@warrane.unsw.edu.au; Anthony.Shannon@uts.edu.au
Research Areas:Mathematics
Web of Science Categories:Mathematics
Multidimensional scaling and visualization of patterns in prime numbers