Maybe I should put this in the cacti and succulent forum?

I think it is Mammillaria hahniana. Hard to say which subspecies.

Thanks Thijs van soest! I like the look of those flowers on the hahniana! Hopefully I can get it blooming! I just bought it today there was quite a good selection too, I tend to be drawn towards any cacti that has that white look! Very nice!!

In your climate you want to give it is as much sunlight as you can, keep it as warm as you can and water very sparingly. They tend to flower in late winter/early spring here and can go on for a while, but getting them to flower in non-ideal conditions can be hard. Here is an exceptional example of the flowering display they can put on - though this plant came without a name tag so the ID is tentative. The flowers were not quite all the way open because the plant was in the shade when I took the picture. This plant kept on flowering from early March till some time in May before it went dormant for summer.

Very nice Thijs, quite a good size too, mine is only about fist size! I see they can be prolific bloomers even when young so thats good news! It'll go with my others on a S/E facing window (best I have) although I doubt any cactus from the shop I bought it in has ever experienced natural sun I'll have to be careful! So no cooler period needed for bloom? Very helpful Thijs thankyou.

It might need a cooler period in its normal environment, but where you are at warm days are probably still on the 'cool' side for these plants. For example, I just spent 2.5 weeks vacationing in the UK (mainly Wales and Scotland) and the highest temperature we experienced ~75F was still lower than the night time lows here in the Phoenix area during the same period.
Winter lows here are rarely below freezing, over the last few years maybe a couple of days with light frost every winter, most of the time day time highs still in the 60s, so in my yard they never really get very cold for very long and they flower just fine.

Yea that sounds about right! Average night temps here during fall are about 50°f 90% humidity! Not so great lol

That humidity was what bothered us during our trip, even though we were never really warm or hot, we were still sweating all the time. Not used to the humidity anymore - we get some in July and August, but nothing like the constant humidity over there (I am originally from the Netherlands so at one point in my life I was used to it, but not anymore).

Good luck with the cacti!

Yes thisj fingers crossed... thankyou for the info.