The idea is to get a large number that is relatable to humans. The number of atoms in the observable universe is estimated at around 10^80, but this number isn't satisfying as the universe is made up of more than "atoms". So instead I'd like to an estimate of the number of "white light" photons we'd have if the universe's mass and energy were converted to be exclusively made up of them.
Attempted working (because you people always want that):
To solve this:
A) What is the average energy of visible light, of what we perceive to be white light?
B) How much energy is there in the universe?
C) Divide B by A. (The result should be higher than 10^80.)
A) Visible light is anything between 1.65eV and 3.10eV, so the answer is somewhere between these values. Naively we could average this to 2.375 eV (and I'll use this number for my calculation below).
However, as I understanding it, what we perceive as white light, in daylight conditions, is the visible spectrum of roughly 5500K black body radiation (which has more energy on the blue side). I'm not sure how we'd get the average eV of it.
If you have another standard measure of "white" sunlight, I could be happy with that too.
B) According to this page from cornell, the observable universe, including dark matter, is 3 x 10^55 g. I'm not sure if this includes dark energy (68% of the universe), or any other energy (if that's even significant).
One gram contains 900,000,000,000,000,000,000 ergs of energy (9x10^20) via this page at stanford, or 5.6e+32 eV (converted by google calculator). So if we multiple grams with energy per gram, the universe contains 3 x 10^55 * 5.6 x 10^32 eV. That gives us 1.68 x 10^88 eV.
C) 1.68 x 10^88 eV / 2.375 eV gives a final result of 7 x 10^87.
That's seven orders of magnitude greater than the number of atoms in the universe, so it appears to be in the right ballpark.
However my answer is using some rough or uncertain figures, and I'm not certain of my working, so I'm after a more precise answer.