The prime 1366733339 can be peeled down to a single digit by removing one digit at a time from either end to make a sequence of primes 136673333, 36673333, 3667333, 667333, 66733, 6673, 673, 67, 7.
Determine the largest integer for which this is possible.
The program builds rather than peels. It uses unsigned 64-bit integers so as to expand the allowable size without sacrificing speed, but even then it is slow and is possibly limited by the size of numbers it allows.
clearvars
global p mx build
mx=0;
for p=[2 3 5 7]
build=uint64(p);
addon
end
function addon
global p mx build
for front=[true false]
if front
digset=uint64(1):9;
else
digset=uint64([1 3 7 9]);
end
for newdig=digset
pSave=p; buildSave=build;
if front
% p=str2uint64([num2str(newdig) num2str(p)]);
sss=['p=uint64(' num2str(newdig) num2str(p) ');'];
eval(sss);
else
p=10*p+newdig;
end
if isprime(p)
if p>=mx
mx=p;
disp(p)
for i=length(build):-1:1
disp(build(i))
end
% disp(' ')
end
build=[build p];
addon;
end
p=pSave; build=buildSave;
end
end
end
finds the following, which is near the limit of unsigned 64-bit integers:
9813229623122317339
813229623122317339
81322962312231733
1322962312231733
322962312231733
32296231223173
3229623122317
229623122317
29623122317
2962312231
962312231
62312231
6231223
231223
31223
1223
223
23
2
Note that due to time constraints it only shows series build on the first prime, 2. It does however, as mentioned, get close to the limit of the variable type used.
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Posted by Charlie
on 2024-05-30 09:02:46 |
computer exploration
