Hello Community , im new here and want to factor a prime factor of 512 bit
i can input here this key so that all can access to it ?

NFS@Home pretty much only accepts numbers that have some sort of mathematical interest. I don't speak for Greg, but it's unlikely you'll convince anyone to break an RSA key for you.

Only RSA-1024, RSA-2048 and RSA-4096 has yet to be factorized.

If you mean the numbers from the old RSA contest, actually there are many numbers up to 2048 bits that have not been factored. It's true there hasn't been an RSA-type key larger than RSA768 (publicly) factored since 2010.

Please have me excused, but I had to look up "512-bit number".

Apparently there is a fact that there is no single RSA-512, RSA-768, RSA-1024, RSA-2048 or RSA-4096 number. For each RSA designation, there happens to be several such numbers, probably less of them the higher you go.

This number is an example of a RSA-155 and is consisting of 155 decimal digits:

109417386415705274218097073220403576120037329454492059909138421314763499842889
34784717997257891267332497625752899781833797076537244027146743531593354333897

Its factors are

102639592829741105772054196573991675900716567808038066803341933521790711307779

and

106603488380168454820927220360012878679207958575989291522270608237193062808643


http://en.wikipedia.org/wiki/RSA_numbers#RSA-155


So why not try factoring

77904004346346670503878542786396000104129136321344930547891284768371445950925377
67310826689425715004160093034133595468941695387445233512928852161531387989

instead.

It is a RSA-512 number and apparently has not been factored yet.

Should I perhaps make a check on the PRP1073 that is around here?

Where is the dancing lady (or woman) located / or to be found?

512 bits is not large enough to require NFS@Home; a single machine can do the job in a few core-weeks.