SB Sieving and factoring gaps analysis 1000.000T < p < 2000.000T (0.3M < n < 3.0M)

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Last Update: Fri 14-Jan-2005 09:11 (GMT)


RATIO:   1000000.00G - 1052221.26G,  size:52221.26G,  est fact: 116   (1000000000000000-1052221264335247) R:15.734, S: 0.100
RATIO:   1052221.26G - 1082426.70G,  size:30205.44G,  est fact:  64   (1052221264335247-1082426703649429) R: 8.846, S: 0.056
RATIO:   1082426.70G - 1120003.21G,  size:37576.50G,  est fact:  83   (1082426703649429-1120003208235859) R:10.635, S: 0.068
RATIO:   1125827.87G - 1261544.08G,  size:135716.22G,  est fact: 347   (1125827868651313-1261544084928181) R:34.103, S: 0.217
RATIO:   1261544.08G - 1590402.92G,  size:328858.83G,  est fact: 715   (1261544084928181-1590402916048273) R:65.548, S: 0.416
RATIO:   1590402.92G - 2000000.00G,  size:409597.08G,  est fact: 673   (1590402916048273-2000000000000000) R:88.583, S: 0.386


Gaps found: 6
Gaps size:  994175.34G (99.42%)
Factors in range: unique:8, duplicate:5, excluded:56
Factors missing (estimated): 1998 - 11777


Smallest gap between factors:       350252052062 (1120090945654001 - 1120441197706063)
Largest (accepted) gaps between factors

       : 1121288.46G - 1124002.99G,  size: 2714.53G,                  (1121288457993413-1124002986931039) R: 0.766, S: 0.005
       : 1124397.82G - 1125205.47G,  size:  807.65G,                  (1124397822980423-1125205472513623) R: 0.228, S: 0.001
       : 1120441.20G - 1121080.29G,  size:  639.09G,                  (1120441197706063-1121080291950193) R: 0.181, S: 0.001
       : 1120090.95G - 1120283.77G,  size:  192.83G,                  (1120090945654001-1120283772044243) R: 0.055, S: 0.000
       : 1124234.39G - 1124346.41G,  size:  112.03G,                  (1124234386814243-1124346413224427) R: 0.032, S: 0.000
       : 1125277.73G - 1125384.89G,  size:  107.16G,                  (1125277732748629-1125384892353173) R: 0.030, S: 0.000
       : 1125479.96G - 1125560.21G,  size:   80.24G,                  (1125479961733703-1125560205821437) R: 0.023, S: 0.000
       : 1124002.99G - 1124077.45G,  size:   74.47G,                  (1124002986931039-1124077453568143) R: 0.021, S: 0.000
       : 1121090.82G - 1121160.26G,  size:   69.44G,                  (1121090819487497-1121160263904929) R: 0.020, S: 0.000
       : 1124107.09G - 1124174.18G,  size:   67.09G,                  (1124107091428723-1124174178778873) R: 0.019, S: 0.000



Key:
SERIES  Gap was found by examining gaps sizes of previous 30 factors.
RATIO   Gap was found by examining previous gap size.
SER+RAT Gap was found by both SERIES and RATIO methods.
#*#     Gap has been identified in a range declared [complete].

Please note that gaps in completed ranges are not an immediate cause for concern.
This may be due to a delay in the user submitting factors, or may be an acceptable
gap, and I simply need to adjust the thresholds.  If you feel a gap is larger than
you would anticipate for a given p, please e-mail or PM the user concerned.



Using limits:
   Range (p): 1000000.00G - 2000000.00G
   Range (n): 0.30M - 3.00M
   LIMIT_P_RATIO: 317.00
   SERIES_SIZE: 30.00
   SERIES_LIMIT: 3.50
   K: ALL