# How to make a Monte carlo simulation for identifying prime numbers with a non-100% probability

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Petch Anuwutthinawin on 8 Jul 2021
Answered: Steven Lord on 8 Jul 2021
%Scenario:
%straight line of squares, 1-250. you start at random point.
%move left or right (50 50 chance).
%If on square 1, only move to 2. If on 250, only move to 249.
%Look at NEW number, and bleat or not.
%If on prime number, 'bleat' 85% of the time.
%If not prime, 'bleat' 30% of the time
%Find PROBABILITY that in a 15 move sequence, 'bleat' 4<x<9 times in a row.
%Plot convergence for the probability, should be approx 19.125%.
%How do I make the bleat or not section work? How do I loop this enough
%times to show convergence? Is this supposed to use a monte carlo
%simulation?
%% Making the first move.
Bleat=0;
for start==1:250
for start=randi(250,1,1) %for a random starting tile
G=rand;
if G>0.5;
FrstMove=start+1 %moves left or right 50% chance
else
FrstMove=start-1
end
if start==1; %to ensure that 1 can only move to 2
FrstMove=2
end
if start==250; %to ensure that 250 can only move to 249
FrstMove=249
end
%% Bleat or not
if FrstMove==2 || 3 || 5 || 7 || 11 || 13 || 17 || 19 || 23 || 29 || 31 || 37 || 41 || 43 || 47 || 53 || 59 || 61 || 67 || 71 || 73 || 79 || 83 || 89 || 97 || 101 || 103 || 107 || 109 || 113 || 127 || 131 || 137 || 139 || 149 || 151 || 157 || 163 || 167 || 173 || 179 || 181 || 191 || 193 || 197 || 199 || 211 || 223 || 227 || 233 || 239 || 241 && G<=0.85;; %prime number (?)
Bleat=Bleat+1 %should be if it is prime (in the list) and G<=0.85 it bleats. Does not run correctly.
elseif FrstMove~=2 || 3 || 5 || 7 || 11 || 13 || 17 || 19 || 23 || 29 || 31 || 37 || 41 || 43 || 47 || 53 || 59 || 61 || 67 || 71 || 73 || 79 || 83 || 89 || 97 || 101 || 103 || 107 || 109 || 113 || 127 || 131 || 137 || 139 || 149 || 151 || 157 || 163 || 167 || 173 || 179 || 181 || 191 || 193 || 197 || 199 || 211 || 223 || 227 || 233 || 239 || 241 && G<=0.3; %is not prime
Bleat=Bleat+1 %bleats 30% of the time if NOT prime. This elseif does not run correctly.
end
disp(Bleat) %display bleat in sequential order in the 15 loop sequence.
end
%% final probability
True=0
if bleat= %how to write bleat 4<x<9 times in a row?
True=True+1
Prob=True/ %total number of trials
end
##### 2 CommentsShowHide 1 older comment
Petch Anuwutthinawin on 8 Jul 2021
It is a question. I do not know why the written code does not work and I want help to fulfill the criteria of the problem.

Steven Lord on 8 Jul 2021
This section of code (shortened quite a bit) doesn't do what you think it does.
% if FrstMove==2 || 3
You expected this to be true if either FrstMove was equal to 2 or FrstMove was equal to 3. Let's see what it does when FrstMove was equal to 5.
FrstMove = 5;
if FrstMove==2 || 3
disp("Condition satisfied")
else
disp("Condition NOT satisfied")
end
Condition satisfied
That's because your condition is equivalent to:
% if (FrstMove==2) || 3
In the example above (FrstMove == 2) is false (since FrstMove is 5) but 3 is true (since it's not 0.) So false || true is true.
What you likely want to use is ismember.
FrstMove = 5;
if ismember(FrstMove, [2 3])
disp("Condition satisfied")
else
disp("Condition NOT satisfied")
end
Condition NOT satisfied
Of course since this isn't a primality testing code, you could just use isprime.
FrstMove = 5;
if isprime(FrstMove)
disp("Condition satisfied")
else
disp("Condition NOT satisfied")
end
Condition satisfied

Walter Roberson on 8 Jul 2021
if FrstMove==2 || 3 || 5 || 7 || 11 || 13 || 17 || 19 || 23 || 29 || 31 || 37 || 41 || 43 || 47 || 53 || 59 || 61 || 67 || 71 || 73 || 79 || 83 || 89 || 97 || 101 || 103 || 107 || 109 || 113 || 127 || 131 || 137 || 139 || 149 || 151 || 157 || 163 || 167 || 173 || 179 || 181 || 191 || 193 || 197 || 199 || 211 || 223 || 227 || 233 || 239 || 241 && G<=0.85;; %prime number (?)
MATLAB does not have any numeric distributive comparison operators. You have to specify every test individually. Your code first compares a variable to 2, giving back 0 (false) or 1 (true). It then encounters the double | which is short-circuit "or". If the comparison to 2 was true then the if succeeds without evaluating the rest. If the comparison to 2 failed then it evalutes the 3 as a logical value. Values are considered true if they are nonzero and since 3 is nonzero it is considered true, and the double | succeeds.
The code does not compare the variable to 2 and then 3 and then 5 and so on. If you want to do that then I suggest using ismember()