JLPT level 2 kanji and the kyouiku kanji

Are the kanji used for the JLPT level two the same as the 1,000 kanji kids learn in elementary school(kyouiku kanji)?
Would it be good for me to study only those kanji?

I believe that for JLPT level 2, about 1,000 kanji, those learned by 6th grade by school children in Japan, should be OK, though I'm not sure exactly which ones those are.

BTW, for studying or living in Japan, you should go for "joyo" kanji, which I believe there are currently 1945 of. Those are the ones commonly used in general newspapers.

As far as I know, the JLPT2 kanji are 740: 576 are taught in elementary school (1-6 grade), whereas the remaining 164 in junior high school.

JLPT3 and JLPT4 are respectively 165 and 79. These kanji are all taught in elementary school.

Finally, additional 185 kanji are taught in elementary school but they are not included in the above JLPT levels.
I hope these figures are correct.

but if you include the level 3 and 4 kanji, wouldn't that be all 1,000 of the kyoiku kanji plus other joyo kanji?

JLPT2+JLPT3+JLPT4 are 985 kanji covering "only" 821 kyoiku kanji (which are 1006 in total). Just as an example, there are 6 kanji taught in 2 elementary that surprisingly are in JLPT1 set.