Exploding CPU

The well known hardware manufacturing company *Processors
for Professors* is about to release a highly specialized
CPU with exceptional functionality in, amongst other areas,
number theory. It has, for example, an instruction PFACT that takes one parameter and returns
all prime factors of that parameter, with an outstanding
execution speed. It has, however, one considerable problem. The
scientists at the testing lab has just found out that the
PFACT instruction for some
special input values freaks out and makes the entire processor
explode. Even though this could be an amusing effect, it is not
the way it was intended to work. The skilled mathematicians
have, by trial and error, found that the explosive numbers all
share the same interesting number theoretic properties, which
might be of help when troubleshooting.

An explosive number is a number $x=p_0 p_1 p_2 \dots p_ n$ where all $p_ i$s are distinct prime numbers such that $p_ i = Ap_{i-1}+B$ for $i=1,2,\dots ,n$. $n \geq 3$, $p_0 \equiv 1$. A and B are always integers, and might be different for different explosive numbers.

For example, the processor will explode when factorizing the number $4505$, because $4505 = 1 \cdot 5 \cdot 17 \cdot 53$ and $5 = 3 \cdot 1 + 2$, $17 = 3 \cdot 5 + 2$ and $53 = 3 \cdot 17 + 2$ and the numbers 5, 17 and 53 are all prime numbers. In this case $A=3$ and $B=2$.

You are kindly asked to write a computer program that will aid this company in estimating the impact of the errors, by calculating the amount of explosive numbers that exists within a given range of integers.

The input starts with a row containing the number $0 \leq N \leq 100$ of test cases that will follow. For each test case, there will be one row containing two integers, $x_ L$ and $x_ H$ separated by a single space. These numbers are such that $0 \leq x_ L \leq x_ H \leq 2,000,000,000$.

For each test case, output the number of explosive numbers that exist in the range $x_ L \leq x \leq x_ H$.

Sample Input 1 | Sample Output 1 |
---|---|

2 4505 4505 0 5000 |
1 5 |