Thanks to http://www.peaklist.org/ for the data.
List of the peaks shown on the map
(name prominence/height)
Mt. Everest 8848/8848, Aconcagua 6962/6962, Denali (Mt. McKinley) 6138/6194, Kilimanjaro 5885/5895, Cristobal Colon 5509/5700, Mt. Logan 5250/5959, Pico De Orizaba (Citlaltepetl) 4922/5636, Vinson Massif 4892/4892, Puncak Jaya 4884/4884, Gora Elbrus 4741/5642, Mont Blanc 4696/4809, Damavand 4667/5610, Klyuchevskaya Volcano 4649/4750, Nanga Parbat 4608/8125, Mauna Kea 4205/4205, Jengish Chokusu (ex. Pik Pobedy) 4148/7439, Chimborazo 4122/6267, Bogda Shan 4122/5445, Namcha Barwa 4106/7782, Kinabalu 4095/4095, Mt. Rainier 4023/4393, K2 4017/8611, Ras Dejen 3980/4533, Volcan Tajumulco 3980/4220, Pico Bolivar 3957/4981, Mt. Fairweather 3955/4671, Yu Shan 3952/3952, Ngaliema (Mt. Stanley) 3951/5109, Kangchenjunga 3922/8586, Tirich Mir 3910/7708, Mt. Cameroon 3901/4040, Mt. Kenya 3825/5199, Gunung Kerinci 3805/3805, Mt. Erebus 3794/3794, Fuji San 3776/3776, Mt. Cook 3755/3755, Jebel Toubkal 3755/4167, Cerro Chirripo 3727/3820, Gunung Rinjani 3726/3726, Pico Teide 3718/3718, Monte San Valentin 3696/4058, Gunnbjørnsfjeld 3694/3694, Nevado Ojos Del Salado 3688/6893, Gunung Semeru 3676/3676, Mt. Blackburn 3535/4996, Kongur Shan 3585/7649, Mt. Ararat (Agri Dagi) 3611/5137, Minya Konka 3642/7556, Ritacuba Blanco 3645/5410, Finisterre Range Hp 3675/4125