From the picture it is a model 530J which is apparently 32-bit but oddly with Execute Disable Bit (XD/NX-bit), while 531 which is also 3GHz added the 64-bit capability. It would probably work in your motherboard but 530J is not on the
officially supported list while 531 is. In any case you don't need a 32-bit processor to run a 32-bit OS, 64-bit processors work fine.
Technically, 90nm Prescott all included the EM64T instructions but it was disabled in all the 1M L2 cache models except 5x1, 517, 524 models. The 2M L2 cache models N0 stepping and later for desktops also support 64-bit (P4 HT 620, 630, 640, 650, 660, 662, 670, 672). All of the 65nm Cedar Mill CPUs support 64-bit and have 2MB L2 cache (P4 HT 631, 641, 651, 661)
All of the "Pentium D" dual-core Pentium 4 including 90nm Smithfield (2 x 1MB L2 cache) and 65nm Presler (2 x 2MB L2 cache) appear to support 64-bit.
Note this is fine for running
XP-64 or 64-bit
Win 7 or even
Win 8 as all have XD/NX-bit + CMPXCHG16b, but as far as I'm aware only the 65nm models have PREFETCHh/PrefetchW and LAHF/SAHF for 64-bit
Win 8.1 and
Win 10
Your board does support Presler but
I don't why you'd bother when it also supports
Core 2 Duo and related
Pentium Dual-Core CPUs, which are way faster in games and by now the same price of almost free + shipping. Pentium 4 architecture required special compilers to perform at its best and no software uses those kinds of optimizations anymore.