They accumulated the third highest total in their first-class history before declaring on 694-9, with Leicestershire closing on 86-1 in their second innings and trailing by 270.
Simpson finished with 205 not out, having shared a seventh-wicket partnership of 255 with Danny Lamb, of which 134 was also a career high.
Ari Karvelas scored 55 and that was with his dismissal six overs after the tea Sussex declared with a first innings lead of 55 356 in reply to Leicestershire's 338, with 24 overs remaining.
There was barely a hint of a breakthrough until five hours after lunch when Lamb, on 85, came to a leg-edge delivery from Matt Salisbury but Ben Cox could only help reach the limit.
Simpson reached his fifty off 108 balls and his hundred off 197, reaching the biggest milestone when he turned Salisbury for his 15th four. The shot took Sussex 450 up to make good measure.
Lamb was faster to a hundred than his partner by some distance, needing only 108 balls, adding 10 fours to the four sixes.
He hit the scoop for six number five off Ben Mike , bowling Liam Trevaskis high over long-off to score 500 with his sixth maximum and sweeping Louis Kimber for his seventh He was, however, bowled while attempting to lift Trevaskis at mid-wicket.
Jack Carson then hit two sixes in a 23-ball 38 and Simpson added five sixes in 23 fours, his second hundred coming from 97 balls, before to put an end to the innings that...
They accumulated the third highest total in their first-class history before declaring on 694-9, with Leicestershire closing on 86-1 in their second innings and trailing by 270.
Simpson finished with 205 not out, having shared a seventh-wicket partnership of 255 with Danny Lamb, of which 134 was also a career high.
Ari Karvelas scored 55 and that was with his dismissal six overs after the tea Sussex declared with a first innings lead of 55 356 in reply to Leicestershire's 338, with 24 overs remaining.
There was barely a hint of a breakthrough until five hours after lunch when Lamb, on 85, came to a leg-edge delivery from Matt Salisbury but Ben Cox could only help reach the limit.
Simpson reached his fifty off 108 balls and his hundred off 197, reaching the biggest milestone when he turned Salisbury for his 15th four. The shot took Sussex 450 up to make good measure.
Lamb was faster to a hundred than his partner by some distance, needing only 108 balls, adding 10 fours to the four sixes.
He hit the scoop for six number five off Ben Mike , bowling Liam Trevaskis high over long-off to score 500 with his sixth maximum and sweeping Louis Kimber for his seventh He was, however, bowled while attempting to lift Trevaskis at mid-wicket.
Jack Carson then hit two sixes in a 23-ball 38 and Simpson added five sixes in 23 fours, his second hundred coming from 97 balls, before to put an end to the innings that...
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