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Old 2022-10-03, 12:45   #67
mart_r
 
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Quote:
Originally Posted by Bobby Jacobs View Post
You should get paid for this.
For that comment? Yeah, that was a tremendous outburst of creativity possibly worthy of a Pulitzer
But you lifted my mood, so I give a small update.
Prime scarcities with CSG > 1 are hard to find these days, but recently I got pn = 205,465,264,987,331 which has
CSG = 1.0024950 for k = 927,
CSG = 1.0028949 for k = 941, and
CSG = 1.0063712 for k = 939.

Last fiddled with by mart_r on 2022-10-03 at 12:49
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Old 2022-10-16, 22:22   #68
Bobby Jacobs
 
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You should get paid for all of the work you do in finding prime numbers.
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Old 2022-10-17, 11:50   #69
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The replies that I get mean more to me than any amount of money (which is too tight to mention anyway ).
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Old 2022-11-25, 20:57   #70
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Default Eins Zwei Drei Vier Fünf Sechs Sieben Acht

Not a record in terms of CSG, but a close contender - and the largest p for which a CSG (or "scarcity/paucity ratio") > 1 is known:
A region with exceptionally few k+1 consecutive primes for k=274..380 (listed only for CSG > 1)

Code:
k    k-gap  p start          CSG
274  12914  309292876045019  1.00720962
275  12950  309292876045019  1.00580100
276  12996  309292876045253  1.00890285
277  13050  309292876045019  1.01561044
278  13110  309292876045019  1.02503096
279  13156  309292876045093  1.02813121
280  13230  309292876045019  1.04390467
281  13244  309292876045019  1.03252630
282  13300  309292876044949  1.04014280
283  13318  309292876044931  1.03061882
284  13342  309292876044907  1.02384129
285  13398  309292876044731  1.03143202
286  13438  309292876044811  1.03184383
287  13518  309292876044731  1.05023223
288  13542  309292876044707  1.04343738
289  13566  309292876044683  1.03667817
290  13580  309292876044683  1.02549729
291  13590  309292876044673  1.01261680
292  13620  309292876044629  1.00864965
293  13662  309292876044731  1.00999419
294  13700  309292876044731  1.00957620
295  13728  309292876044731  1.00476373
313  14448  309292876045019  1.01377017
314  14462  309292876045019  1.00309794
315  14518  309292876044949  1.01051652
316  14552  309292876045019  1.00847219
317  14604  309292876045019  1.01416841
318  14634  309292876045019  1.01041245
319  14674  309292876044949  1.01095647
320  14736  309292876044731  1.02093989
321  14760  309292876044707  1.01462007
322  14784  309292876044683  1.00833143
323  14840  309292876044731  1.01572021
324  14892  309292876044731  1.02140336
325  14922  309292876044731  1.01768328
326  14960  309292876044731  1.01738801
327  14984  309292876044707  1.01114162
328  15008  309292876044683  1.00492570
331  15134  309292876045019  1.00919910
332  15180  309292876045253  1.01231622
333  15220  309292876045213  1.01289750
334  15256  309292876045177  1.01179308
335  15340  309292876045093  1.03098513
336  15414  309292876045019  1.04600439
337  15432  309292876045019  1.03721965
338  15484  309292876044949  1.04288334
339  15502  309292876044931  1.03413607
340  15526  309292876044907  1.02796453
341  15582  309292876044851  1.03529999
342  15622  309292876044811  1.03588507
343  15702  309292876044731  1.05337889
344  15726  309292876044707  1.04718529
345  15750  309292876044683  1.04102057
346  15768  309292876044683  1.03236619
347  15778  309292876044673  1.02041740
348  15804  309292876044629  1.01519709
349  15832  309292876044601  1.01083020
350  15850  309292876044601  1.00234451
351  15906  309292876044527  1.00959606
352  15924  309292876044527  1.00113860
379  16980  309292876043453  1.00929898
380  16998  309292876043453  1.00114922
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