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A050414 Numbers n such that 2^n - 3 is prime. 35
3, 4, 5, 6, 9, 10, 12, 14, 20, 22, 24, 29, 94, 116, 122, 150, 174, 213, 221, 233, 266, 336, 452, 545, 689, 694, 850, 1736, 2321, 3237, 3954, 5630, 6756, 8770, 10572, 14114, 14400, 16460, 16680, 20757, 26350, 30041, 34452, 36552, 42689, 44629, 50474, 66422, 69337, 116926, 119324, 123297, 189110, 241004, 247165, 284133, 354946, 394034, 702194, 750740 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With 60 known primes for n < 750741, these primes appear to be more common than Mersenne primes.  Of course at this time, the larger terms are only probable primes. - Paul Bourdelais, Feb 04 2012

The numbers 2^n-3 and 2^n-1 both are primes for n = 3, 5, ? The lesser number 2^p-3 is prime for primes p = 3, 5, 29, 233, 42689, 69337, ... - Thomas Ordowski, Sep 18 2015

LINKS

Table of n, a(n) for n=1..60.

PRP Top Records of the form 2^n-3 [From M. Frind & P. Underwood, Gary Barnes, Oct 20 2008]

MATHEMATICA

Do[ If[ PrimeQ[ 2^n -3 ], Print[n]], { n, 1, 15000 }]

PROG

(PARI) for(n=2, 10^5, if(ispseudoprime(2^n-3), print1(n, ", "))) \\ Felix Fröhlich, Jun 23 2014

CROSSREFS

Cf. A045768, A050415, A057732 (numbers n such that 2^n + 3 is prime).

Sequence in context: A047250 A081944 A129948 * A266322 A136681 A206330

Adjacent sequences:  A050411 A050412 A050413 * A050415 A050416 A050417

KEYWORD

nonn

AUTHOR

Jud McCranie, Dec 22 1999

EXTENSIONS

More terms from Robert G. Wilson v, Sep 15 2000

More terms from Andrey V. Kulsha, Feb 11 2001

a(40)=20757, verified with 20 iterations of Miller-Rabin test, from Dmitry Kamenetsky, Jul 12 2008

A new PRP term 26350 from Serge Batalov, Oct 20 2008

Corrected and extended by including two smaller (apparently known) PRP and 16 larger terms from PRP Top Records of this form, all discovered by M. Frind & P. Underwood, Gary Barnes, Oct 20 2008

a(59) and a(60) (corresponding to probable primes since they are PRP 3,5,7) discovered by Paul Bourdelais, Mar 26 2012

STATUS

approved

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Last modified February 21 23:44 EST 2019. Contains 320381 sequences. (Running on oeis4.)