# Proving composite number

• February 14th 2013, 05:15 AM
RuyHayabusa
Proving composite number
How do you prove that 1280000401 is a composite number?
• February 14th 2013, 05:43 AM
lpuchala
Re: Proving composite number
1280000401=421*3040381
• February 15th 2013, 08:42 AM
Soroban
Re: Proving composite number
Hello, RuyHayabusa!

Quote:

How do you prove that 1,280,000,401 is a composite number? . I don't know . . .
Now that Ipuchala has factored it, I see a truly far-fetched approach.

$1,280,\!000,\!401 \;=\;2^7(10^7) + 2^2(10^2)+1 \;=\;20^7 + 20^2 + 1$

. . . . . . . . $421 \;=\;2^2(10^2) + 2(10) + 1 \;=\;20^2 + 20 + 1$

Then: . $(20^7 + 20^2 + 1) \div (20^2+20+1) \;=\;20^5 - 20^4 + 20^2 - 20 + 1$

That is: . $1,\!280,\!000,\!401 \div 421 \;=\;3,\!040,\!381$
• February 16th 2013, 01:20 AM
RuyHayabusa
Re: Proving composite number
Thanks,it really helped!