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The 10^25 stated in the article may be mistakenly using the very similar number for joules of energy created each second by the sun (10^25).

Could they also be using a number for a specific type of neutrino?

That Fermi's lab link says all the neutrinos produced by the sun are of the same type, electron neutrinos.

Parent comment possibly meant "10^25 neutrinos with an energy level indicating they were produced by the CNO process".

After reading the article it seems they were referring to total neutrinos, so I think the OP's correction stands.