Yes - the new State pension works on the basis that 35 years of NICs qualify you for full amount, and 10 years minimum needed to get it at all (with linear decrease where < 35 years). So the above 34/35 fraction looks correct.
Is it worth paying the voluntary contributions for missing years when I am living and working in Ireland?
I have around 15 years of contributions in the UK.
When I retire, will I get both pensions?