Find the greatest prime strictly smaller than a supplied integer. Formula and previous prime remain visible in one place for independent verification.
Previous-prime search moves downward from the integer immediately below the input. It returns the first candidate that satisfies the prime definition.
Below 100, 99 is divisible by three and 98 is even. Ninety-seven passes every required divisor test, so it is the previous prime. This Previous Prime example can be compared with primality check.
Subtract one, skip even candidates other than two, and test divisibility through the square root until a prime is found.
Inputs of two or less have no smaller positive prime. The search excludes the starting number itself.
The result brackets a number from below, helps form prime gaps, and supplies a nearby smaller modulus or factor candidate.
The lower end of the prime sequence is exceptional. Two is the first prime, so a search starting at two or below cannot return a previous positive prime. Above that boundary, checking candidates in descending order guarantees that the first successful test is the greatest qualifying prime.
Keep Starting integer integral when Previous Prime requires integers. Verify the result through the defining Previous Prime identity.
Test zero in Previous Prime, then test one in Previous Prime. Rebuild the starting integer through Previous Prime.
Read Previous prime against Starting integer, not in isolation. Use the fixed condition to estimate the Previous Prime magnitude. When the fixed condition is altered, label the new Previous Prime trial. Its Previous prime should not replace the original Previous Prime answer.
A one-input trial is useful when Previous Prime behaves unexpectedly. Change the fixed condition alone, retain Starting integer and the fixed condition, and observe Previous prime. Multiple simultaneous edits would make the cause of the changed Previous prime ambiguous within the Previous Prime setup.
Keep the input convention with Previous prime so a later Previous Prime review does not assign the number a different meaning.
It is 2.
No positive prime exists below 2.
Yes.
No, the result is strictly smaller.