How long would it take to repopulate the Earth ?
- Starting from a single couple to our present population.
- No diseases or premature deaths taken into account, 60 y.o. lifespan.
- Consanguinity problems ignored.
300 years, give or take a bit.
3000 is more like it. Our present population is highly dependent on our current technology and is not sustainable without it.
50,000 years, same as before. I base this on the fact that our growth since then has been more-or-less constant, minus a Black death or two. Granted, that’s starting from a few hundreds or thousands, not one pair. But close enough.
Also not allowing for people to do nothing but breed, as that’s not realistic.
Back-of-envelope calculation: If food and other essentials are handwaved away then it’s perfectly possible for the population to increase by a factor of four or five in every generation. Say 14 generations at three generations per century, that’s 500 years from a standing start. That’s eight to ten kids per couple, every couple, every generation. You might imagine a faster rate of growth and it’s hard to know exactly where to draw the line.
The OP posited everyone lived till 60. So presumably they have the tech to make that happen.
log(present population)/log(q)=n
where q is the births per-person, n is the number of generations needed to reach the present population starting from just q people. Comes to about 400 years if q=3
Lifespan’s irrelevant, time-of-menopause for women is the determinant (since men are not the limiting factor). Everything after ~45 is not pertinent.
But you need to elaborate on whether this is a simple maths question (in which case the lowball figures like 400 years are more likely) or a practical one (in which case thousands is more likely.) But absent child mortality, I’d say a few thousand years, not hundreds.
Well in the Bible it talks about people living into their 100’s.
A female has what? About 600 eggs? Assuming she could live and breed a long time she could conceivably have hundreds of children.
** MrDibble **
I was looking for a best case scenario, backed with an exponential growth formula, which is what Simplicio has provided.
Life span matters towards the population total, if not fertility rate.
True enough, although only really for the last few populations. Time to first kid, time to menopause are the limiting factors…
She’d have to live past 400 years.
We’re talking hard science here, not mythology. 
While life expectancy has changed quite a bit (especially in the last 100 years in developed countries), life span worldwide has not.
The problem isn’t the number of offspring, but the quality of those children.
With only a single pair of antecedents the chances of a fatal genetic flaw rise in just a few generations.
Cool.
"Consanguinity problems ignored. " says the OP
pop ln years
7,167,300,000 22.693
3 1.099 20.7
3.5 1.253 18.1
4 1.386 16.4 (So 8 kids per couple)
Some spreadsheet work gives me something under 425 years for q=3 and something under 320 years for q=5. I think I’m missing something.
Assuming we still have public health not too long. It wasn’t long ago when having 6-10 kids per couple was normal. If we went back to a TFR of about 8 you’d have population quadruple every 30 years or so. Every 5 generations would increase population by a factor of 1000 or so, so after 16 generations we’d be back to about 7 billions, maybe 300-500 years.
No, I mean, “…and something under 320 years for q=4 (or ave number of kids =8).” Sheesh.
Well that depends. Imagine the earth with less disease since their would have been fewer viruses and bacteria back then. Also no toxic chemicals in the ground, air, or water.