Data commit

Task/Truncatable-primes/MATLAB/truncatable-primes-1.m

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+function largestTruncatablePrimes(boundary)
+
+    %Helper function for checking if a prime is left of right truncatable
+    function [leftTruncatable,rightTruncatable] = isTruncatable(prime,checkLeftTruncatable,checkRightTruncatable)
+
+        numDigits = ceil(log10(prime)); %calculate the number of digits in the prime less one
+        powersOfTen = 10.^(0:numDigits); %cache the needed powers of ten
+
+        leftTruncated = mod(prime,powersOfTen); %generate a list of numbers by repeatedly left truncating the prime
+
+        %leading zeros will cause duplicate entries thus it is possible to
+        %detect leading zeros if we rotate the list to the left or right
+        %and check for any equivalences with the original list
+        hasLeadingZeros = any( circshift(leftTruncated,[0 1]) == leftTruncated );
+
+        if( hasLeadingZeros || not(checkLeftTruncatable) )
+            leftTruncatable = false;
+        else
+            %check if all of the left truncated numbers are prime
+            leftTruncatable = all(isprime(leftTruncated(2:end)));
+        end
+
+        if( checkRightTruncatable )
+            rightTruncated = (prime - leftTruncated) ./ powersOfTen; %generate a list of right truncated numbers
+            rightTruncatable = all(isprime(rightTruncated(1:end-1))); %check if all the right truncated numbers are prime
+        else
+            rightTruncatable = false;
+        end
+
+    end %isTruncatable()
+
+    nums = primes(boundary); %generate all primes <= boundary
+
+    %Flags that indicate if the largest left or right truncatable prime has not
+    %been found
+    leftTruncateNotFound = true;
+    rightTruncateNotFound = true;
+
+    for prime = nums(end:-1:1) %Search through primes in reverse order
+
+        %Get if the prime is left and/or right truncatable, ignoring
+        %checking for right truncatable if it has already been found
+        [leftTruncatable,rightTruncatable] = isTruncatable(prime,leftTruncateNotFound,rightTruncateNotFound);
+
+        if( leftTruncateNotFound && leftTruncatable ) %print out largest left truncatable prime
+            display([num2str(prime) ' is the largest left truncatable prime <= ' num2str(boundary) '.']);
+            leftTruncateNotFound = false;
+        end
+
+        if( rightTruncateNotFound && rightTruncatable ) %print out largest right truncatable prime
+            display([num2str(prime) ' is the largest right truncatable prime <= ' num2str(boundary) '.']);
+            rightTruncateNotFound = false;
+        end
+
+        %Terminate loop when the largest left and right truncatable primes have
+        %been found
+        if( not(leftTruncateNotFound || rightTruncateNotFound) )
+            break;
+        end
+    end
+end

Task/Truncatable-primes/MATLAB/truncatable-primes-2.m

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+>> largestTruncatablePrimes(1e6)
+998443 is the largest left truncatable prime <= 1000000.
+739399 is the largest right truncatable prime <= 1000000.