A003618 Largest n-digit prime.

7, 97, 997, 9973, 99991, 999983, 9999991, 99999989, 999999937, 9999999967, 99999999977, 999999999989, 9999999999971, 99999999999973, 999999999999989, 9999999999999937, 99999999999999997, 999999999999999989, 9999999999999999961, 99999999999999999989

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• nice
• base

Comments

Since 10^n - 1 is always a multiple of 9, one could be tempted to think that 9 is the least frequently occurring least significant digit in terms of this sequence. - Alonso del Arte, Dec 03 2017

The occurrences of least significant digits in the first 8000 terms (see A033874) are 1: 2028, 3: 2032, 7: 2014, and 9: 1926. - Giovanni Resta, Mar 16 2020

Examples

			No power of 10 is prime.
9 = 3^2, 8 = 2^3 but 7 is prime, so a(1) = 7.
99 = 3^2 * 11 but 97 is prime, so a(2) = 97.
999 = 3^3 * 37 but 997 is prime, so a(3) = 997.
9999 = 3^2 * 11 * 101, 9997 = 13 * 769, 9995 = 5 * 1999, 9993 = 3 * 3331, 9991 = 97 * 103, ..., 9975 = 5^2 * 399, but 9973 is prime, so a(4) = 9973.
		

References

• O'Hara, J. Rec. Math., 22 (1990), Table on page 278.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000 (terms 1..200 from T. D. Noe. _Jon E. Schoenfield_ verified that terms 1..200 are indeed primes, Feb 02 2009)
• Eric Weisstein's World of Mathematics, Previous Prime
• R. G. Wilson, v., Extract from letter to N. J. A. Sloane, May 20 1994, with annotated scanned copy of page 278 of O'Hara article.

Crossrefs

Cf. A003617, A033874, A114429 (largest n-digit twin prime).

Programs

Magma

[PreviousPrime(10^n): n in [1..20]]; // Vincenzo Librandi, Sep 13 2016

Maple

a:= n-> prevprime(10^n):
seq(a(n), n=1..20);  # Alois P. Heinz, Feb 11 2021

Mathematica

NextPrime[10^Range[20], -1] (* Harvey P. Dale, Feb 03 2011 *)

PARI

a(n)=precprime(10^n) \\ Charles R Greathouse IV, Jul 19 2011

Python

from sympy import prevprime
print([prevprime(10**n) for n in range(1, 21)]) # Michael S. Branicky, Feb 11 2021

Extensions

More terms from Stefan Steinerberger, Apr 08 2006