PSG news - state of play at end of 2020

Let’s do some end of year celebration of progress

(coped from the Mersenne Forum’s Prime Gap Search group as pertinent to Gapcoin)

2021-02-16, 10:50 Post to Mersenne Forum PSG: “Let’s do some end of year celebration of progress”

Let’s do some end of year celebration of progress.

I’ll update these in late December

• by year merit status
• prime gap animation

I calculated

• Number of updates this year >12,000!
• Largest merit this year (Seth’s 38.0479)
• largest gap found this year (Martin’s 1898630)
• Smallest update to a record (#173, Gapcoin +0.00025 merit)
• Smallest gap updated this year (Rob Smith’s 1906 merit 26.7)

I still need to find

• largest update to a record (Probably 122542 14.5 -> 28.1 merit)
• largest gap with an update
• Total merit improved this year

Any other fun statistics people would like me to calculate?

Humblebrag: I submitted 1340 records for 4441# and 930 for 2221# with an average merit of 20.8 and 24.37 respectively.

$ sqlite3 gaps.db 'SELECT startprime FROM gaps' | 
sed -n 's!^[^/]*[^0-9/]\([0-9]\+#\).*!\1!p' |
sort | uniq -c | sort -nr |
awk '$1 > 200 { ("sqlite3 gaps.db \"SELECT discoverer, count(*),round(max(merit),2),round(avg(merit),2) \
FROM gaps WHERE startprime like \\\"%" $2 "%\\\" GROUP BY 1 ORDER BY 2 DESC LIMIT 1\"") |
getline freq; print($0 "\t" freq); }'

count primorial  Who|HowManyTheydid|MaxMerit|AvgMerit
   1391 4441#    S.Troisi|1340|28.98|20.82
   1002 2221#    S.Troisi|930|33.03|24.37
    962 9439#    Jacobsen|868|24.27|16.32
    923 6761#    Jacobsen|911|25.2|17.67
    786 49999#    Rosnthal|786|25.86|12.62
    736 4139#    Jacobsen|714|27.0|20.05
    579 9973#    Rosnthal|525|25.17|16.41
    535 10343#    Jacobsen|528|25.55|16.37
    400 6199#    DStevens|370|27.27|18.99
    376 6661#    S.Troisi|322|27.31|18.02
    371 5003#    Jacobsen|343|26.42|19.71
    351 9629#    RobSmith|269|26.52|16.87
    276 4409#    Rosnthal|229|27.07|19.95
    228 18481#    PierCami|226|19.12|12.15

Seth subsequently noted:

I updated two tables on the lists site

“Top 20 gaps by merit” is now “Top 20 largest gaps ordered by merit”

“Top 20 overall merits” is now “Top 20 overall merits [plus 50th,100th,200th,…,500th]”

I also added a weighted average line to the merit plot on cloudygo and min_x, max_x input.

You can see where the focused efforts from gapcoin & S.Troisi have increased average merit in the neighborhood of 5000-6000 and 45000-52000