Previous Prime
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A003618/M4452, A007917, and A033874 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
19-1-2021
1511
Previous Prime
The previous prime function 
gives the largest prime less than 
. The function can be given explicitly as
where 
is the 
th prime and 
is the prime counting function. For 
, 4, ... the values are 2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, ... (OEIS A007917).
The previous prime function was implemented in versions of the Wolfram Language prior to 6 as PreviousPrime[n] (after loading the package NumberTheory`NumberTheoryFunctions).
Finding the previous prime before 
gives the largest 
-digit prime. For 
, 2, ..., the first few of these are 7, 97, 997, 9973, 99991, 999983, 9999991, 99999989, ... (OEIS A003618). The amounts by which these are less than 
are 3, 3, 3, 3, 27, 9, 17, 9, 11, 63, ... (OEIS A033873).
REFERENCES:
O'Hara, F. "More Prime Trivia." J. Recr. Math. 20, No. 3, 209-210, 1988.
O'Hara, F. "The Smallest and Largest 
-Digit Primes for 
." J. Recr. Math. 22, No. 4, 277-279, 1990.
Ondrejka, R. "Prime Trivia." J. Recr. Math. 14, No. 4, 285, 1981-1982.
Sloane, N. J. A. Sequences A003618/M4452, A007917, and A033874 in "The On-Line Encyclopedia of Integer Sequences."
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