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### Paper:

TR99-010 | 1st April 1999 00:00

#### A Lower Bound for Primality

TR99-010
Authors: Eric Allender, Igor E. Shparlinski, Michael Saks
Publication: 6th April 1999 11:55
Keywords:

Abstract:

Recent work by Bernasconi, Damm and Shparlinski
proved lower bounds on the circuit complexity of the square-free
numbers, and raised as an open question if similar (or stronger)
lower bounds could be proved for the set of prime numbers. In
this short note, we answer this question affirmatively, by showing
that the set of prime numbers (represented in the usual binary
notation) is not contained in \$\acp\$ for any prime \$p\$. Similar
lower bounds are presented for the set of square-free numbers, and
for the problem of computing the greatest common divisor of two numbers.

### Comment(s):

Comment #1 to TR99-010 | 21st June 1999 16:41

#### An Improvement Comment on: TR99-010

Comment #1
Authors: Eric Allender
Accepted on: 21st June 1999 16:41