A professor can have a 5 by 5 professors cube but it’s not a necessity . It would just be nice. If I read papers in atomic physics and do some simulations and teach lectures, I can become a professor too. I can also become one in any area in Arxiv. Rubiks cube Notebook. Chess cube softwares. Just search magic cube and chess.com and lichess on smartphone. Gabbasoft on PC attached in link below..
2 by 2 RURiURUURi RiFRiBBRFiRiBBRRUi abcd 3 by 3 FFULRiFFLiRUFF abcdefgh 3 mins 30 s Has D U F B L R 4 by 4 Centres ridirUridr Edges RFiUF dRFiURiFdi Parity 1 : 2r2B2Ul2Uri2Ur2Ur2U2Fr2Fli2B2r Parity 2: 2RDi2R2r2U2F2r2F2U2R2rD2R parity 3 : 2r2U2r2U2u2r2u abcdefghijklmnop abcdefghijkl 6 +3*2 23 min 54 secs Has D U F B L R D1 D2 L1 L2 F1 F2 [[4,4],[4,3],[3,4]] 5 by 5 Edges : (Uu1)’RUR’(u1U) Parity : (Ll)’U2(Ll)’U2F2(Ll)’F2(Rr)U2(Rr)’U2(Ll)2 26 mins 15 seconds Has D U F B L R D1 D2 D3 L1 L2 L3 F1 F2 F3 abcdefghijklmnopqrstuvwx abcdefghijklmnop [[5,5],[4,5],[5,4]] 7 by 7 1 2 3 4=2inv 5 =1inv 6=2 7=3inv 8=4 1 2 3 2’ 1’ 2 3’ 4 hrs 30 mins [[7,7],[7,6],[6,7]] 9 by 9 7 hrs 11 mins Has D U F B L R D1 D2 D3 D4 D5 L1 L2 L3 L4 L5 F1 F2 F3 F4 F5 [[9,9],[9,8],[8,9]] 20 by 20 aza7z7 aza3z3 1000 by 1000 10^18 A big number 10^(10^10)