# Counterexample Help

• Sep 28th 2010, 10:11 PM
MATNTRNG
Counterexample Help
Find a counterexample to the following assertion:

Every odd number can be expressed as the sum of a power of 2 and a prime.
• Sep 28th 2010, 10:18 PM
Prove It
• Sep 28th 2010, 10:38 PM
chisigma
5=2+3... and 3 is prime...

Kind regards

$\chi$ $\sigma$
• Sep 28th 2010, 10:40 PM
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Quote:

Originally Posted by MATNTRNG
Find a counterexample to the following assertion:

Every odd number can be expressed as the sum of a power of 2 and a prime.

Haha, 1.
• Sep 28th 2010, 10:48 PM
Prove It
Quote:

Originally Posted by chisigma
5=2+3... and 3 is prime...

Kind regards

$\chi$ $\sigma$

Haha I forgot about $2^1$.

But yeah, 1 would work ;)
• Oct 4th 2010, 09:32 AM
chisigma
The smallest odd number > 1 that can't be written as the sum of a power of 2 and a prime number is 127...

127-1= 126= 2 x 7 x 9

127-2 = 125 = 5 x 5 x 5

127-4 = 123 = 3 x 41

127 - 8 = 119 = 7 x 17

127 - 16 = 111 = 3 x 37

127 - 32 = 95 = 5 x 19

127 - 64 = 63 = 3 x 3 x 7

Kind regards

$\chi$ $\sigma$
• Oct 5th 2010, 05:26 AM
chisigma
There are seventeen odd numbers >1 and <1000 that can't be written as the sum of a power of 2 and a prime number:

127,149,251,331,337,373,509,599,701,757,809,877,90 5,907,959,977,997...

Kind regards

$\chi$ $\sigma$
• Oct 5th 2010, 09:24 AM
wonderboy1953
Quote:

Originally Posted by MATNTRNG
Find a counterexample to the following assertion:

Every odd number can be expressed as the sum of a power of 2 and a prime.

If you're only allowing positive numbers and addition, then 1 and 3 would fill that bill.