# Is this method of proving non-regularity is equivalent to pumping lemma?

I find it really difficult to prove non-regularity of a language using pumping lemma. I do understand that regular language is the language that can be expressed using DFA/RE. So if I can't create DFA/RE for language can I use that as proof of it's non regularity?

For example, following is an attempt to create a DFA for
0^P
where p is prime number.

Following machine accepts 2,3,5,7 which are primes. But it also accepts those which are not primes. Can it be considered as proof of non regularity of said language?

• "So if I can't create DFA/RE for language can I use that as proof of it's non regularity?" -- If you can prove that you can't, yes. Just being unable to is only a proof for irregularity or lacking creativity/skill. So, have another shot (or two) at the Pumping lemma; objectively, it's not that hard. There are other methods as well. See our reference question. – Raphael Jun 9 '15 at 7:24

Here is how your method of proof works on the (regular) language $\{0^2,0^3,0^5,0^7\}$. I tried to construct a DFA for this language – the DFA accepting all strings, but while it accepts $0^2,0^3,0^5,0^7$, it also accepts other strings. What when wrong?
To prove that a language is not regular, we have to show that it is impossible to construct a DFA for it. Having tried and failed is not enough – maybe it's just difficult? For example, people believe that P$\neq$NP, but so far we haven't been able to prove this. Does this show that P=NP?