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?]