Primmer's men beat Burgess Hill by six wickets after posting 217-4.
They skittled the visitors for 166. Chris Hayden (45), Dave Leaver (65 not out) and Joe Seaman (48) were among the runs. Primmer took 7-62.
Clymping continued their impressive form with a sixth successive win to ensure they finish fourth.
They scored 224-5 and then bowled Southwick out for 172.
Captain Ben Challen played a major role with a season-best 134 not out followed by 4-38.
Gary Tester took two wickets, Adam Tester and Karl Pierce one apiece. Two Southwick batsmen were run out and Dave Blackall took a good catch.
Challen said: "It is a good finish to the season. That's a plus and hopefully we can win again this week to close the gap on Arundel.
"Everyone is playing with confidence and if we can keep the team together and add a few new players over the winter then we should do well next season."
Relegated Eastergate scratched their penultimate match at Ifield.
The second relegation spot will be finalised when Burgess Hill host Southwick this weekend. Anything less than a win for the Wickers means they will go down.
Richard Nichols scored 60 for Ansty at home to Keymer and Hassocks in division two but, apart from a cameo 27 from Andy Hadfield, the home team were dismissed for 130. Colin Faith and Jamie Tatford took three wickets apiece. In reply, Keymer lost three wickets in reaching the modest target (134-3). John Carr was undefeated on 43, Andy Rimmer scored 27 and skipper John Price made 25.
Champions Broadwater completed their league campaign with another convincing victory against second-placed Crawley who slipped to fourth.
The visitors batted first and a promising 54-run fourth-wicket partnership between Gul Khan and Aamir Riaz was broken by the division's leading wicket taker, Joe Owen, who went on to finish with 43 league scalps. Crawley lost their last six wickets for only 13 runs and slumped to 103 all out.
Broadwater openers Bob Reynolds and Neal Jones completed their third 50th partnership in four weeks before Richard Iago and Owen knocked off the winning runs.
Goring were held at home by Henfield after scoring 229-7. Andy Duke top scored with 107 not out, Neil Pierce took 5-30. The visitors were 194-9 in reply with Chris Crampton hitting 80 and Graham Fuller 49.
Barns Green are third from bottom following their draw at Pulborough. Green made 204-4 thanks to Roger Southgate (93 not out) and John Filby (44). The home side were 167-9, Clint Astridge making 51 and Andy Simmonds 41.
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