I think someone on Mathematics would be able to answer this question best; mathematicians never say bigger number. I cannot put my finger on it either but to say that, colloquially, bigger is a psychical size; larger is a quantity.
What follows is basically a cut and paste from englishforums.com -user Terr3
(I'm not sure how great this can possibly be considering all the grammar and spelling mistakes I cleaned up):
When we say "slightly higher register", we are referring to the social context in which we use the words -- not the meaning of the words. If you speak with the president of a country you will probably use "high register", for example.
-A large amount of light has penetrated through tree leaves.
-A great amount of light has penetrated through tree leaves.
Concluding that 'large' and 'great' are interchangeable but not 'big'
when it comes to indicating math or quantity.
-A big success (correct)
-A large success (wrong)
-A great success (correct)
Concluding that 'great' and 'big' could be interchangeable when
objective has no physical scale.
-It's no big deal (correct)
-It's no great deal (wrong)
-It's no large deal (wrong)
-He has suffered a great deal of stress(correct)
-He has suffered a large deal of stress(wrong)
-He has suffered a big deal of stress (wrong)
Concluding that since 'deal' is a unit without physical scale,
'great' and 'big' are interchangeable, except for the case of 'big
deal'. I think 'big deal' is a jest of incorrect grammar to highlight
the sarcastic tone.
-He is a big guy (correct)
-He is a great guy (correct but yielded a different meaning)
Concluding that 'great' can only have an equal meaning to 'big' when it comes to quantity, outside of that the meaning is 'good'
Also concluding that 'large' and 'big' are interchangeable at any
object with a physical size.
Being a native speaker I've never had to consider it in such detail,
so I think we may have to accept this provisionally. There always seem
to be counterexamples in English.