- Feb 15, 2014Good find! And, your copy and paste looks accurate.From the AMS paper I see that starting at prime = 31 is a first occurrence where the least number solution is not prime. In that case, the least number solution is 307271 = 109 • 2819, and the least prime solution is 366791.Out of curiosity I decided to continue with my investigation past prime 19, up to prime 31, because I was curious. Namely, would the least number that can't be written as the sum of two 31-smooth numbers correspond to the least number solution (307271) or the least prime solution (366791) ?It turns out, neither!The first 5 integers > 1 that can't be written as the sum of two 31-smooth numbers are
118271, 236542, 307271, 354813, 366791.

118281 = 101*1171.

Go figure...

Mark

---In primenumbers@yahoogroups.com, <david.broadhurst@...> wrote:

From

D. H. Lehmer, Emma Lehmer and Daniel Shanks

http://www.ams.org/mcom/1970-24-110/S0025-5718-1970-0271006-X

R. F. Lukes, C. D. Patterson and H. C. Williams

http://www.ams.org/mcom/1996-65-213/S0025-5718-96-00678-3

it seems that the continuation of

http://oeis.org/A002223/b002223.txt

is as follows:

27 33857579279

28 89206899239

29 121560956039

30 328878692999

31 328878692999

32 513928659191

33 4306732833311

34 4306732833311

35 4306732833311

36 8402847753431

37 70864718555231

38 317398900373231

39 501108392233679

40 501108392233679

41 501108392233679

42 501108392233679

43 5551185799073591

44 5551185799073591

45 5551185799073591

46 7832488789769159

47 7832488789769159

48 102097158739597271

49 102097158739597271

50 315759454565514431

51 868116409360316399

52 3412527725201978759

53 3546374752298322551

54 3546374752298322551

55 3546374752298322551

56 3546374752298322551

57 3546374752298322551

However this needs checking by someone

better at cutting and pasting than I.

David (struggling with abominable yahoo interface) - << Previous post in topic Next post in topic >>