How to resolve the algorithm Prime conspiracy step by step in the PARI/GP programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Prime conspiracy step by step in the PARI/GP programming language
Table of Contents
Problem Statement
A recent discovery, quoted from Quantamagazine (March 13, 2016): and
The task is to check this assertion, modulo 10. Lets call i -> j a transition if i is the last decimal digit of a prime, and j the last decimal digit of the following prime.
Considering the first one million primes. Count, for any pair of successive primes, the number of transitions i -> j and print them along with their relative frequency, sorted by i . You can see that, for a given i , frequencies are not evenly distributed.
(Modulo 10), primes whose last digit is 9 "prefer" the digit 1 to the digit 9, as its following prime.
Do the same for one hundred million primes.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Prime conspiracy step by step in the PARI/GP programming language
Source code in the pari/gp programming language
conspiracy(maxx)={
print("primes considered= ",maxx);
x=matrix(9,9);cnt=0;p=2;q=2%10;
while(cnt<=maxx,
cnt+=1;
m=q;
p=nextprime(p+1);
q= p%10;
x[m,q]+=1);
print (2," to ",3, " count: ",x[2,3]," freq ", 100./cnt," %" );
forstep(i=1,9,2,
forstep(j=1,9,2,
if( x[i,j]<1,continue);
print (i," to ",j, " count: ",x[i,j]," freq ", 100.* x[i,j]/cnt," %" )));
print ("total transitions= ",cnt);
print(p);
}
primes considered= 1000000
2 to 3 count: 1 freq 0.000100 %
1 to 1 count: 42853 freq 4.29 %
1 to 3 count: 77475 freq 7.75 %
1 to 5 count: 0 freq 0 %
1 to 7 count: 79453 freq 7.95 %
1 to 9 count: 50153 freq 5.02 %
3 to 1 count: 58255 freq 5.83 %
3 to 3 count: 39668 freq 3.97 %
3 to 5 count: 1 freq 0.000100 %
3 to 7 count: 72828 freq 7.28 %
3 to 9 count: 79358 freq 7.94 %
5 to 1 count: 0 freq 0 %
5 to 3 count: 0 freq 0 %
5 to 5 count: 0 freq 0 %
5 to 7 count: 1 freq 0.000100 %
5 to 9 count: 0 freq 0 %
7 to 1 count: 64230 freq 6.42 %
7 to 3 count: 68595 freq 6.86 %
7 to 5 count: 0 freq 0 %
7 to 7 count: 39604 freq 3.96 %
7 to 9 count: 77586 freq 7.76 %
9 to 1 count: 84596 freq 8.46 %
9 to 3 count: 64371 freq 6.44 %
9 to 5 count: 0 freq 0 %
9 to 7 count: 58130 freq 5.81 %
9 to 9 count: 42843 freq 4.28 %
total transitions= 1000001
15485917
time = 5,016 ms.
You may also check:How to resolve the algorithm Smith numbers step by step in the Quackery programming language
You may also check:How to resolve the algorithm Reverse a string step by step in the REBOL programming language
You may also check:How to resolve the algorithm Exponentiation order step by step in the D programming language
You may also check:How to resolve the algorithm Floyd's triangle step by step in the 360 Assembly programming language
You may also check:How to resolve the algorithm Jewels and stones step by step in the Modula-2 programming language