used FLOOR(1052 + RAND() * 3564)
to create a random value and it seems to be working. Here is the final piece.
SET @query = CONCAT("
SELECT SQL_NO_CACHE * INTO OUTFILE '/Users/Admin/logs/General_Log/log_",
DATE_FORMAT(NOW(),"%M-%d-%y_%h-%m-%s_"), FLOOR(1052 + RAND() * 3564), ".csv'",
"
FIELDS TERMINATED BY ','
ENCLOSED BY '\"\'",
"LINES TERMINATED BY '\\n\'",
"FROM mysql.general_log;");
PREPARE statement FROM @query;
EXECUTE statement;
SELECT @query;