User:Karbon

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Babel user information
de-N Dieser Benutzer spricht Deutsch als Muttersprache.
en-3 This user has advanced knowledge of English.
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Admin of this Wiki.

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PHP example

number = 1234567.896

Number format English (en): 1,234,567.90

Example table for Sierpinski/Riesel problems

Data explantation

Data given in the table:

  • base b and some data for this base
    • conjectured k (CK) and the covering set in {}
    • algebraic factors (if exist) and k-values with these
    • remaining k-values or proven and search range in [] sorted by GCD
    • 10 highest primes/PRPs

[...]

Colors used

      proven and all primes are defined primes
      proven but some primes are only probable primes that have not been certified
      unproven

Table

Base Data
2 78557 {3, 5, 7, 13, 19, 37, 73}
GCD = 1: 21181, 22699, 24737, 55459, 65536 [8.589G], 67607 (other k at n=31M)
10223(31172165), 19249(13018586), 27653 (9167433), 28433 (7830457), 33661 (7031232), 5359 (5054502), 4847 (3321063), 54767 (1337287), 69109 (1157446), 65567 (1013803)
3 11047 {2, 5, 7, 13, 73}
GCD = 2: 1187, 1801, 3007, 3047, 3061, 3307, 5321, 5743, 5893, 6427, 6569, 6575, 7927, 8161, 8227, 8467, 8609, 8863, 8987, 9263, 9449 (all at n=10K)
621(20820), 10243(9731), 2747(7097), 10207(6089), 823(6087), 10741(6028), 821(5512), 5147(5153), 9721(5040), 41(4892)
4 419 {3, 5, 7, 13}
none - proven
186(10458), 94(291), 176(228), 129(207), 89(167), 86(108), 174(103), 369(71), 101(66), 293(58)
5 7 {2, 3}
none - proven
4(2), 3(2), 6(1), 5(1), 2(1), 1(1)
6 174308 {7, 13, 31, 37, 97}
113 k's remain (k = 1296 at n=268.4M, k = 1814 at n=12K, other k = 4 mod 5 at n=2.2K, other k at n=2M)
139413(1279992), 33706(910462), 125098(896696), 31340(833096), 59506(780877), 10107(559967), 113966(511831), 172257(349166), 121736(298935), 124221(278517)
105 319 {2, 53}
none - proven (with probable primes that have not been certified: k = 191)
191 (5045), 36 (675), 39 (348), 264 (275), 183 (210), 150 (193), 80 (177), 164 (146), 167 (140), 204 (105)