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User:J. Lowell

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I was born in 1985. I first knew this database in 1997.

List of numbers that produce sequences similar to A152466 (sequences similarly defined that don't appear to yield prime numbers after a finite number of terms):

  1. 322 (Largest known term is a C132 divisible by all prime numbers less than 60 except 47 and 59)
  2. 622 (Largest known term is a C281 divisible by all prime numbers less than 70 except 47, 61, and 67)
  3. 664 (Largest known term is a C131 divisible by all prime numbers less than 30 except 11 and 23)
  4. 776 (Largest known term is a C107 divisible by all prime numbers less than 40 except 29 and 37)
  5. 830 (Largest known term is a C164 divisible by all prime numbers less than 60 except 43 and 59)
  6. 1042 (Largest known term is a C202 divisible by all prime numbers less than 50 except 37 and 43)
  7. 1044 (Largest known term is a C111 divisible by all prime numbers less than 50 except 31, 41, 43, and 47)
  8. 1468 (Largest known term is a C209 divisible by all prime numbers less than 20 except 17 and 19)
  9. 1556 (Largest known term is a C125 divisible by all prime numbers less than 50 except 37 and 47)
  10. 1690 (Largest known term is a C124 divisible by all prime numbers less than 60 except 53 and 59)
  11. 1858 (Largest known term is a C149 divisible by all prime numbers less than 70 except 53 and 67)
  12. 1898 (Largest known term is a C209 divisible by all prime numbers less than 80 except 59 and 79)
  13. 1960 (Largest known term is a C109 divisible by all prime numbers less than 50 except 23, 41, and 43)
  14. 2248 (Largest known term is a C175 divisible by all prime numbers less than 50 except 31, 41, and 47)
  15. 2304 (Largest known term is a C150 divisible by all prime numbers less than 50 except 23, 43, and 47)
  16. 2312 (Largest known term is a C252 divisible by all prime numbers less than 50 except 19 and 47)
  17. 2328 (Largest known term is a C108 divisible by all prime numbers less than 40 except 29 and 37)
  18. 2490 (Largest known term is a C179 divisible by all prime numbers less than 20 except 17 and 19)
  19. 2506 (Largest known term is a C169 divisible by all prime numbers less than 40 except 29, 31, and 37)
  20. 2596 (Largest known term is a C153 divisible by all prime numbers less than 50 except 41, 43, and 47)
  21. 2716 (Largest known term is a C119 divisible by all prime numbers less than 80 except 41, 71, and 73)
  22. 2824 (Largest known term is a C236 divisible by all prime numbers less than 50 except 41, 43, and 47)
  23. 2924 (Largest known term is a C115 divisible by all prime numbers less than 50 except 37 and 47)
  24. 2972 (Largest known term is a C130 divisible by all prime numbers less than 50 except 31 and 41)
  25. 3038 (Largest known term is a C113 divisible by all prime numbers less than 20 except 17 and 19)
  26. 3110 (Largest known term is a C269 divisible by all prime numbers less than 70 except 47, 61, and 67)
  27. 3112 (Largest known term is a C171 divisible by all prime numbers less than 30 except 23 and 29)
  28. 3126 (Largest known term is a C95 divisible by all prime numbers less than 30 except 17, 23, and 29)
  29. 3176 (Largest known term is a C223 divisible by all prime numbers less than 40 except 17 and 31)
  30. 3196 (Largest known term is a C145 divisible by all prime numbers less than 40 except 29, 31, and 37)
  31. 3238 (Largest known term is a C227 divisible by all prime numbers less than 50 except 37 and 47)
  32. 3266 (Largest known term is a C169 divisible by all prime numbers less than 50 except 37, 43, and 47)
  33. 3320 (Largest known term is a C131 divisible by all prime numbers less than 30 except 11 and 23)
  34. 3712 (Largest known term is a C105 divisible by all prime numbers less than 40 except 31 and 37)
  35. 3868 (Largest known term is a C107 divisible by all prime numbers less than 40 except 11, 31, and 37)
  36. 4034 (Largest known term is a C115 divisible by all prime numbers less than 40 except 29 and 31)
  37. 4068 (Largest known term is a C339 divisible by all prime numbers less than 70 except 47 and 61)
  38. 4108 (Largest known term is a C141 divisible by all prime numbers less than 60 except 47 and 59)
  39. 4112 (Largest known term is a C119 divisible by all prime numbers less than 40 except 31 and 37)
  40. 4298 (Largest known term is a C221 divisible by all prime numbers less than 40 except 23 and 31)
  41. 4354 (Largest known term is a C281 divisible by all prime numbers less than 50 except 19 and 47)
  42. 4378 (Largest known term is a C129 divisible by all prime numbers less than 30 except 17 and 23)
  43. 4528 (Largest known term is a C169 divisible by all prime numbers less than 40 except 31 and 37)
  44. 4622 (Largest known term is a C153 divisible by all prime numbers less than 40 except 37, 41, and 47)
  45. 4668 (Largest known term is a C126 divisible by all prime numbers less than 50 except 37 and 47)
  46. 4696 (Largest known term is a C356 divisible by all prime numbers less than 70 except 59 and 67)
  47. 4730 (Largest known term is a C203 divisible by all prime numbers less than 60 except 29 and 53)
  48. 4754 (Largest known term is a C146 divisible by all prime numbers less than 50 except 31 and 43)
  49. 4880 (Largest known term is a C126 divisible by all prime numbers less than 50 except 37 and 41)
  50. 4906 (Largest known term is a C316 divisible by all prime numbers less than 50 except 29 and 41)
  51. 4980 (Largest known term is a C159 divisible by all prime numbers less than 50 except 23 and 47)
  52. 5044 (Largest known term is a C150 divisible by all prime numbers less than 50 except 41, 43, and 47)
  53. 5210 (Largest known term is a C202 divisible by all prime numbers less than 70 except 43 and 61)
  54. 5220 (Largest known term is a C221 divisible by all prime numbers less than 50 except 41 and 47)
  55. 5242 (Largest known term is a C229 divisible by all prime numbers less than 60 except 43 and 59)
  56. 5292 (Largest known term is a C111 divisible by all prime numbers less than 40 except 11, 31, and 37)
  57. 5318 (Largest known term is a C166 divisible by all prime numbers less than 40 except 29 and 31)
  58. 5474 (Largest known term is a C132 divisible by all prime numbers less than 50 except 37 and 47)
  59. 5560 (Largest known term is a C125 divisible by all prime numbers less than 40 except 31 and 37)
  60. 5624 (Largest known term is a C149 divisible by all prime numbers less than 20 except 11 and 13)
  61. 5644 (Largest known term is a C159 divisible by all prime numbers less than 50 except 23 and 47)
  62. 5694 (Largest known term is a C209 divisible by all prime numbers less than 80 except 59 and 79)
  63. 5704 (Largest known term is a C270 divisible by all prime numbers less than 70 except 59 and 61)
  64. 5818 (Largest known term is a C317 divisible by all prime numbers less than 60 except 47 and 59)
  65. 5834 (Largest known term is a C162 divisible by all prime numbers less than 40 except 31 and 37)
  66. 5858 (Largest known term is a C186 divisible by all prime numbers less than 50 except 37, 41, and 47)
  67. 6084 (Largest known term is a C143 divisible by all prime numbers less than 60 except 47 and 59)
  68. 6102 (Largest known term is a C141 divisible by all prime numbers less than 50 except 23 and 47)
  69. 6114 (Largest known term is a C244 divisible by all prime numbers less than 40 except 29 and 31)
  70. 6432 (Largest known term is a C110 divisible by all prime numbers less than 40 except 23 and 29)
  71. 6530 (Largest known term is a C185 divisible by all prime numbers less than 40 except 31 and 37)
  72. 6542 (Largest known term is a C445 divisible by all prime numbers less than 90 except 61 and 89)
  73. 6676 (Largest known term is a C236 divisible by all prime numbers less than 40 except 23, 31, and 37)
  74. 6696 (Largest known term is a C160 divisible by all prime numbers less than 50 except 19, 43, and 47)
  75. 6754 (Largest known term is a C221 divisible by all prime numbers less than 40 except 23 and 31)
  76. 6786 (Largest known term is a C123 divisible by all prime numbers less than 40 except 19, 31, and 37)
  77. 6936 (Largest known term is a C252 divisible by all prime numbers less than 50 except 19 and 47)
  78. 6944 (Largest known term is a C123 divisible by all prime numbers less than 40 except 19 and 37)
  79. 7048 (Largest known term is a C136 divisible by all prime numbers less than 40 except 31 and 37)
  80. 7112 (Largest known term is a C125 divisible by all prime numbers less than 50 except 29 and 47)
  81. 7180 (Largest known term is a C134 divisible by all prime numbers less than 30 except 23 and 29)
  82. 7226 (Largest known term is a C168 divisible by all prime numbers less than 60 except 41, 53, and 59)
  83. 7294 (Largest known term is a C202 divisible by all prime numbers less than 50 except 37 and 43)
  84. 7352 (Largest known term is a C89 divisible by all prime numbers less than 40 except 23 and 31)
  85. 7384 (Largest known term is a C229 divisible by all prime numbers less than 80 except 59 and 73)
  86. 7538 (Largest known term is a C196 divisible by all prime numbers less than 60 except 29, 53, and 59)
  87. 7570 (Largest known term is a C119 divisible by all prime numbers less than 30 except 17, 19, and 23)
  88. 7706 (Largest known term is a C189 divisible by all prime numbers less than 70 except 41 and 67)

Note that there's no set rule for the magnitude where I get stuck using http://www.alpertron.com.ar/ECM.HTM

For 6542's sequence, I don't get stuck until I reach a number with 445 digits.

For 3126's sequence, I get stuck at a number with only 105 digits.

UPDATE 17 For some reason or another, Java no longer works well on my computer, so I can no longer do this.

UPDATE #2

Now I can do this again. (3112 is the first number I got after this update.)

UPDATE #3

Google Chrome will soon no longer support Java, so I can no longer do this.

UPDATE #4

For the time being, I'll be able to do this. But after a while, I'll have to switch to Firefox.

UPDATE #5

Alpertron is switching to JavaScript. It hasn't done so yet with the ECM page; I'll have to wait until it does so to continue.

UPDATE #6

Alpertron finally switched to JavaScript.

UPDATE #7

Contrary to my initial speculation, Alpertron hadn't yet switched to JavaScript on its ECM page. It still uses Java, and if it's late at switching, I might have to switch to Firefox for ECM.

UPDATE #8

Alpertron finally switched to HTML5. Contrary to an idea floating in my mind, the switch doesn't make it take less time; it actually made it take MORE time, because Java uses 64-bit variables and JavaScript uses 32-bit variables.

UPDATE #9

Alpertron made several updates so that it can take as little time as it did with Java. So I can find more terms once again.

UPDATE #10

After 81 terms, I'll stop until I learn someone has eliminated one term. I chose this point because it's when the terms become denser than the square numbers (6542 is less than 6561.) Whenever possible, someone please try to eliminate at least one of the values in this list.

UPDATE #11

After Alpertron made it a little easier to factor some numbers between 90 and 120 digits within an hour, 1066 was removed from the list. The C111 that took more than 325 curves finally factored after a few more; the next term after it (a P138) is prime!

UPDATE #12

Once again I had to stop after 82 terms; 6676 is less than 6724. Anyone yet able to eliminate any other terms of this list??

UPDATE #13

I also removed 2144, which was formerly stuck at a C104; I took it past the C104 (via other terms) to a P240.

UPDATE #14

After removing 2144, the list has only 81 terms, and I found an 82nd term at 6696. But 6696 is still less than 6724, so the list still doesn't qualify for more than 82 terms.

UPDATE #15

Somehow, today I found out that 4146 must have been a mistake. I re-did it today and it ended with a P128.

UPDATE #16

Taking 4146 out once again took the total number of terms back down to 81, so now I can add an 82nd term. It's 6722, which is still less than 6724.

UPDATE #17

After triple-checking, 4554 was also taken out. It ended with a P126.

UPDATE #18

After removing 4554, the sequence once again has 81 terms, and when I got to an 82nd term, the term I found was 6754, which is >= 6724. Later I'll add the 83rd term.

UPDATE #19

I found an 83rd term; 6786. Because 6786 is less than 6889, the list doesn't qualify for more than 83 terms.

UPDATE #20

For 5220, a C106 was factored successfully, so I'll continue to see if a prime will occur after a while.


UPDATE #21

Unfortunately, after factoring the C106 of 5220's sequence, it did NOT take me to a prime number after finding a few more terms. The composite number it took me to that it didn't reveal any factors of has 221 digits.

UPDATE #22

The C122 that 5624 originally got stuck on was also factored successfully. So the sequence can continue. Stay tune for update #23, which will reveal the result of the extension; that is, the first term that it doesn't find a factor of easily.

UPDATE #23

After extending 5624's sequence to 2 more terms, there's now a C149 where I get stuck easily.

UPDATE #24

I'm now ready to extend 5858's sequence to whatever extent is possible.

UPDATE #25

After extending 5858's sequence past a C98, I got stuck at a C186.

UPDATE #26

6114's sequence, which got stuck at a C215, is now available again. It took more than 2 hours, but it succeeded. Update #27 should reveal the status of where it gets stuck.

UPDATE #27

After just 2 more terms, 6114's sequence is once again stuck, this time at a C244.

UPDATE #28

After doing 6722 again, this time with a double-check, it was ruled out because the sequence actually ended with a P53.

UPDATE #29

After extending this list to an 83rd term, I found that it's 6936, which is >= 6889, so this list now qualifies for an 84th term; stay tuned.

UPDATE #30

I took the list to an 84th term; 6944. This is unfortunately too small for me to continue past 84 terms (6944 < 7056.)

UPDATE #31

I ruled out 4366 based on someone's suggestion of the smallest factor of the C85; it terminated with a P154.

UPDATE #32

I added an 84th term, 7048. But this is still less than 7056, so I can't continue past this point.

UPDATE #33

Because Alpertron's applet is going more quickly now, some of these are actually easier to extend than they used to be. This allowed 5728's sequence to terminate with a P123; letting me eliminate 5728 and thus reducing the total to 83 terms; stay tuned; I'll add an 84th and probably an 85th term next.

UPDATE #34

I added 7112 as the new 84th term. Because 7112 >= 7056, I can now put an 85th term.

UPDATE #35 I added an 85th term; 7180. But I can't go past this point because 7180 < 7225.

UPDATE #36 I extended 6542's sequence to a C445; thus allowing 6542 to bypass 4696 (whose sequence is stuck on a C356) as having the record magnitude.)

UPDATE #37 I also allowed 6640's sequence to terminate with a P129, so once again the list is back down to 84 terms; I'll add an 85th term soon.

UPDATE #38' I added 7226 as the 85th term; 7226 >= 7225 so now I can put an 86th term in.

UPDATE #39 Now I added 7294 as the 86th term; but 7294 < 7396 so the list once again doesn't qualify past this point.

UPDATE #40 Now 252 and 2772 have been removed because of an update.

UPDATE 41 Because 7294 is only the 84th term now as opposed to the 86th term, I can now extend it to an 85th term; 7352. 7352 >= 7225 so an 86th term can be added as well.

UPDATE 42 I added 7384 as an 86th term. However, 7384 is still < 7396 so I still can't go past this point.

UPDATE 43 Remove 1120 because a P382 has been revealed as its final term. Also checked for a new 86th term and it is known that there are no more less than 7468.

UPDATE 44 I added 7538 as the 86th term. Because 7538 > 7396, the list now qualifies for an 87th term.

UPDATE 45 I added 7570 as the 87th term. Because 7570 > 7569, the list qualifies for an 88th term.

UPDATE 46 I added 7706 as the 88th term, but this list doesn't qualify past this point because 7706 < 7744.

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