Sunday, September 17, 2017

Graph of frequencies of seq numbers. High points occur when final digits of prime numbers contain no repetitions in 4 consecutive primes. Comes from prime4seq1.bas. (114,97) is the highest point. Means there were 97 instances of 114 as sequNumber for a consecutive group of four. 114 in hex is $72 = Bin 0111 0010. This represents the four hex digits 01 11 00 10 which means the four possible rhs digits for primes ( 1,3,7,9) come in this sequence        3   9   1   7.
Really low frequencies occur when there's repletion eg  only one instance in the 6000-odd primes in the first 64k numbers of 7777 -> 10 10 10 10 =$AA .So 4 7's in a row only occurs once in primes in 1-64K.
(What's probability that a 256 sided die will come up with AA only once in 6000 tosses?) [Or, what's probability,on the other hand that $72 will occur 97 times?]

Wednesday, August 30, 2017

Take three consecutive prime numbers and make a triangle out of them. Check the change in the angle opposite the smallest side. As the primes get bigger, their differences seem to matter less and the three sides make an (almost) equilateral triangle. So the angle approaches 60 degrees or Pi/3 radians.

Here's the graph of a few values :