Problems & Puzzles: Conjectures Conjecture 14. Enoch Haga Observation about Palprimes Patrick De Geest has been collecting the quantity of Palprimes of every (odd) length. Please see here. The results of this collection up today are:
Enoch Haga had the inspired idea of multiplying this two columns to get a third one: “the number of digits in the total palprimes of each length”:
Can you see it?… can you see the rate of growth of the numbers of the last column?… it’s around 10 (ten) !!!… Enoch Haga wrote [Feb 28, 1999] to Patrick: “I'm surprised to see that the successive number of digits in the total of palprimes from 1digit to 17digits seems to increase by approximately a constant multiplier of 10. E.g. 45 is ~ 10*4 = 40 (45 actual), 465 is ~ 10*45 = 450 (465 actual), and so on [Sloane A039657]…” Enoch, immediately realized the predictive capability of his discovery and added: “… Therefore, it is easy to guess at the approximate number of 19digit and 21digit palprimes (I will not hazard a guess beyond that!). Simply divide the estimated total number of digits by the number of digits; thus 4597688420/19 = ~ 241.983.600 19digit palprimes. The same procedure yields an estimate of ~ 2.189.370.676 21digit palprimes.” Questions:
*** Jud McCranie has obtained an explanation of the Enoch's observation. Here is his explanation: 1.
P(D), the quantity of primes of D digits is given by: then: D*Ppal(D) = (10 D/(D1)) * 10^((D+1)/2) /(9*ln(10)) This answer the two questions posed. *** 




