MySql 百千万级别数据中随机获取一条或多条记录之RAND()优化

最近所做读书小程序中需从千万条数据中随机抽取一条名言语录展示，常规的select * from famous order by RAND() LIMIT 1;，缺少索引及全表扫描，速度异常慢。
SELECT * FROM famous AS t1 JOIN (SELECT ROUND(RAND() * ((SELECT MAX(id) FROM famous)-(SELECT MIN(id) FROM famous))+(SELECT MIN(id) FROM famous)) AS id) AS t2 WHERE t1.id >= t2.id ORDER BY t1.id LIMIT 1;