Here I have analysed your blog entry sentence by sentence.
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 On the move..



In the recent past I had developed a new hobby.


"In the recent past" It's much quicker to say "Recently".   | "I had developed a new hobby." I *have* developed. Or you could say "I've developed".


Whenever I look at a number I try to find the largest prime factor of the number.

"Whenever I *see* a number I try to find the largest prime factor of *that* number."


Sometimes the number itself happens to be the largest prime factor.

This sentence is fine.


I was on a short walk after dinner last Saturday. Then I saw the number of my neighboring block 403.


The grammar is fine, but it could be joined with the next sentence using a commar (,).

"I was on a short walk after dinner last Saturday, when I saw the number of my neighboring block, 403."


It is the largest prime number I had ever encountered during my random hunt.

*have* instead of had. The words "I" and "have" can be contracted to "I've"

Why is it a "random" hunt?

"It's the largest prime number I've ever encountered during my hunt."


I logged into #math and asked people to tell the largest prime number they know.

Almost. "I logged into #math and asked people to tell *me* the largest prime number they know."

1003, 7, xxxxx, are the answers I got in #math.

Use "and" and don't put a commar (,) after "xxxxx".

"1003, 7 and xxxxx are the answers I got in #math."


1003 happens to be the largest prime number in my memory as of now.

While this sentence is correct, it could be shortened.

"1003 is the largest prime number I know of".


Here's the improved version:
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Recently, I've developed a new hobby. Whenever I see a number I try to find the largest prime factor of that number. Sometimes the number itself happens to be the largest prime factor. I was on a short walk after dinner last Saturday, when I saw the number of my neighboring block, 403. It's the largest prime number I've ever encountered during my hunt. I logged into #math and asked people to tell me the largest prime number they know. 1003, 7 and xxxxx are the answers I got in #math. 1003 is the largest prime number I know of.