At present, a * * * has found 47 perfect numbers. (See Baidu Encyclopedia for details)

The list is as follows:

(2^2- 1)*2^ 1

(2^3- 1)*2^2

(2^5- 1)*2^4

(2^7- 1)*2^6

(2^ 13- 1)*2^ 12

(2^ 17- 1)*2^ 16

(2^ 19- 1)*2^ 18

(2^3 1- 1)*2^30

(2^6 1- 1)*2^60

(2^89- 1)*2^88

(2^ 107- 1)*2^ 106

(2^ 127- 1)*2^ 126

(2^52 1- 1)*2^520

(2^607- 1)*2^606

(2^ 1279- 1)*2^ 1278

(2^2203- 1)*2^2202

(2^228 1- 1)*2^2280

(2^32 17- 1)*2^32 16

(2^4253- 1)*2^4252

(2^4423- 1)*2^4422

(2^9689- 1)*2^9688

(2^994 1- 1)*2^9940

(2^ 1 12 13- 1)*2^ 1 12 12

(2^ 19937- 1)*2^ 19936

(2^2 170 1- 1)*2^2 1700

(2^23209- 1)*2^23208

(2^44497- 1)*2^44496

(2^86243- 1)*2^86242

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^

(2^- 1)*2^