Tool to search for prime numbers located before a number, or the nth previous prime number smaller than/inferior to a given number.
Previous Prime Number - dCode
Tag(s) : Arithmetics
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For a given number $ N $, the previous prime number is the smallest number strictly less than $ N $ which is a prime number.
No mathematical formula allow an automatic calculation of the prime number preceding any number N (less than N). dCode performs primality tests on numbers below the requested number until a prime number is found.
Example: The largest prime number that precedes 100 is 97
Example: The 10th prime number preceding 1000 is 937 (so there is a list of 9 prime numbers between 938 and 999 included)
The number $ N $ must be a positive real number superior to 3.
The largest number with $ n $ digits is $ 10^n -1 $ (that is always a multiple of 9), so the largest prime number with $ n $ digits is the prime number that precedes $ 10^n-1 $.
Example: The largest 4-digit number is $ 10^4 -1 = 10000-1 = 9999 $ so the largest prime number with $ n $ digits is the prime number preceding $ 10000 $ that is $ 9973 $.
The first 20 prime numbers in this list are: 7 (largest 1 digit prime), 97 (largest 2-digit prime), 997 (largest 3-digit prime), 9973, 99991, 999983, 9999991, 99999989, 999999937, 9999999967, 99999999977, 999999999989, 9999999999971, 99999999999973, 999999999999989, 9999999999999937, 99999999999999997, 999999999999999989, 9999999999999999961, 99999999999999999989 etc.
A prime number and the previous prime number are twins primes when their difference equals 2.
Example: 17 and 19 are called twin primes as 19-17 = 2.
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Cite as source (bibliography):
Previous Prime Number on dCode.fr [online website], retrieved on 2023-02-08,