Problems & Puzzles: Puzzles

Puzzle 901. A question about consecutive integers

Abhiram R. Devesh sent the following puzzle.

The following pairs of consecutive numbers n and n+1 have the property that the largest prime factor of n and n+1 is less than the ln(n) and ln(n+1) respectively

eg. 

2400, 2401 ==> (2,3,5), (7) ==> 5 < ln(2400) and 7 < ln(2401)
 

4374, 4375 ==> (2,3), (5,7) ==> 3 < ln(4374) and 7 < ln(4375)

 
Questions
 
Q1: Find the next pair.

Q2: Are there any triplets?
 


Contributions came from Fred Schneider and Simon Cavegn

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Fred wrote:

The question is answered here http://oeis.org/A147302

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Simon Cavegn wrote:

I found no other consecutive pair (yet).
Searched all integers up 4400000000000000.
It's way faster to multiply prime powers than trying factorization.
Check up to 4400000000000000 took 8s, and found 16152018 numbers with largest prime factor < ln(n)

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