Hello Math-Fun Any legal movement of a chess piece can be coded by a 4-digit integer with the traditional convention of square labeling: two digits for the starting square, two digits for the arrival square (1181 would be a Rook movement, for instance, going from a1 to h1). Question #1 What is the finite set of all such legal chess movements/integers? I guess we would (lexicographically) start the collection with: 1) Legal movements starting on the square 11: 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1121, 1122, 1123, 1131, 1132, 1133, 1141, 1144, 1151, 1155, 1161, 1166, 1171, 1177, 1181, 1188; 2) Legal movements starting on the square 12: 1211, 1213, 1214, 1215, 1216, 1217, 1218, 1221, 1222, 1223, 1224, 1231, 1232, 1233, 1234, 1242, 1245, 1252, 1256, 1262, 1267, 1272, 1278, 1282; 3) Legal movements starting on the square 13: 1311, 1312, 1314, etc. (...) 64) Legal movements starting on the square 88: 8811, 8818, 8822, 8828, 8833, 8838, 8844, 8848, 8855, 8858, 8866, 8867, 8868, 8876, 8877, 8878, 8881, 8882, 8883, 8884, 8885, 8886, 8887. Question #2 How many integers of the above set are prime numbers? (those would be called "prime movements") Question #3 What could be the longest "prime tour" made only by distinct prime movements? (This tour would start and stop on the same chessboard's square). Here is an example of a 6-stage such Tour, made by prime numbers taken from the above subset of "prime movements": 1117–1753–5351–5153–5323–2311. Best, É. [With arrows and colors here, on my personal weblog (after the French chess problems part) --cplease rebuild the antispam link by joining the three hereunder segments] http://cinquantesignes. blogspot.com/2020/06/echecs- au-carre.html