Dozenal near- and quasi- repunit primes

[sweety439]

Originally Posted by carpetpool

Srsieve is for numbers of the form k*b^n+-c and sr2sieve requires that k=1 or c=1. Thus, you would have to find a program that sieves your requested forms, or use the -f switch in pfgw instead of a sieve (trial factoring is only slightly slower than actual sieving BTW). Alternatively, you could make a program with GP or some other math library which sieves your specific form. I did this once for other forms that don't have a dedicated sieving program. I could send you an example if you like.

You are wrong, I use -w and sorted by n

Recognized ABC Sieve file:
ABC File
2*12^1729-13 is composite: RES64: [FCBEFF5D9726017B] (0.3088s+0.0442s)
3*12^1729+19 is composite: RES64: [ACD8BE7F69CCF93B] (0.2875s+0.1171s)
3*12^1729+41 is composite: RES64: [13D1BC98F11A1A82] (0.8990s+0.1535s)
6*12^1729+49 is composite: RES64: [3AD5B119E2BC4FE2] (0.2647s+0.1758s)
71*12^1729-5 is composite: RES64: [AA02B20400C7D891] (0.7988s+0.1091s)
128*12^1729-7 is composite: RES64: [C8E3BF8CFD691188] (0.3862s+0.1363s)
3*12^1730-1 is composite: RES64: [1CD2CC9E6C8D8C2C] (0.2181s+0.6109s)
3*12^1730+19 is composite: RES64: [8E72C8EF272B1A9B] (0.7866s+0.1368s)
3*12^1730+41 is composite: RES64: [E12318DFFBE36C71] (0.2949s+0.1277s)
5*12^1730-49 is composite: RES64: [F51EBD81224CFD18] (0.2575s+0.1078s)
10*12^1730-1 is composite: RES64: [4DF840F2E104A15E] (0.3002s+0.1506s)
23*12^1730-1 is composite: RES64: [C6CFD00F72C6845B] (0.3583s+0.1165s)
38*12^1730-5 is composite: RES64: [EBA5F05BB4D8C003] (0.3450s+0.1096s)
62*12^1730-7 is composite: RES64: [50DF9889A454B12B] (0.3860s+0.1197s)
73*12^1730-7 is composite: RES64: [C9B26E9494C4DD5A] (0.3311s+0.1635s)
78*12^1730-1 is composite: RES64: [36209BE0322224D6] (0.2912s+0.1105s)
93*12^1730-5 is composite: RES64: [B98A7200C2AABCC3] (0.3199s+0.0997s)
95*12^1730-7 is composite: RES64: [3344A36EFC545CB9] (0.3698s+0.0004s)

[sweety439]

Originally Posted by sweety439

You are wrong, I use -w and sorted by n

Recognized ABC Sieve file:
ABC File
2*12^1729-13 is composite: RES64: [FCBEFF5D9726017B] (0.3088s+0.0442s)
3*12^1729+19 is composite: RES64: [ACD8BE7F69CCF93B] (0.2875s+0.1171s)
3*12^1729+41 is composite: RES64: [13D1BC98F11A1A82] (0.8990s+0.1535s)
6*12^1729+49 is composite: RES64: [3AD5B119E2BC4FE2] (0.2647s+0.1758s)
71*12^1729-5 is composite: RES64: [AA02B20400C7D891] (0.7988s+0.1091s)
128*12^1729-7 is composite: RES64: [C8E3BF8CFD691188] (0.3862s+0.1363s)
3*12^1730-1 is composite: RES64: [1CD2CC9E6C8D8C2C] (0.2181s+0.6109s)
3*12^1730+19 is composite: RES64: [8E72C8EF272B1A9B] (0.7866s+0.1368s)
3*12^1730+41 is composite: RES64: [E12318DFFBE36C71] (0.2949s+0.1277s)
5*12^1730-49 is composite: RES64: [F51EBD81224CFD18] (0.2575s+0.1078s)
10*12^1730-1 is composite: RES64: [4DF840F2E104A15E] (0.3002s+0.1506s)
23*12^1730-1 is composite: RES64: [C6CFD00F72C6845B] (0.3583s+0.1165s)
38*12^1730-5 is composite: RES64: [EBA5F05BB4D8C003] (0.3450s+0.1096s)
62*12^1730-7 is composite: RES64: [50DF9889A454B12B] (0.3860s+0.1197s)
73*12^1730-7 is composite: RES64: [C9B26E9494C4DD5A] (0.3311s+0.1635s)
78*12^1730-1 is composite: RES64: [36209BE0322224D6] (0.2912s+0.1105s)
93*12^1730-5 is composite: RES64: [B98A7200C2AABCC3] (0.3199s+0.0997s)
95*12^1730-7 is composite: RES64: [3344A36EFC545CB9] (0.3698s+0.0004s)

WTF.... I forget to divide these numbers by 11

[sweety439]

Update the sieve file sorted by exponent. (only for n<=2304, since the original file (n<=12^5) is too large to update here, even when zipped)

[carpetpool]

Originally Posted by sweety439

WTF.... I forget to divide these numbers by 11

How did you sieve them though? I figured you could use the -w option BTW.

[sweety439]

Originally Posted by carpetpool

How did you sieve them though? I figured you could use the -w option BTW.

I sieved start with the prime 13

[sweety439]

Originally Posted by carpetpool

How did you sieve them though? I figured you could use the -w option BTW.

For the form (k*12^n+-c)/11, I sieved k*12^n+-c, since srsieve cannot sieve (k*12^n+-c)/11

[sweety439]

Update the (probable) primes

[sweety439]

Originally Posted by sweety439

These forms have no known (probable) primes:

label     expression
{1}55     (10^n+3E7)/E
{2}97     (2*10^n+695)/E
{8}77     (8*10^n-107)/E
{E}9E     10^n-21
20{E}     21*10^n-1
22{E}     23*10^n-1
34{1}     (309*10^n-1)/E
53{E}     54*10^n-1
89{1}     (804*10^n-1)/E
99{1}     (8E4*10^n-1)/E

However, except the first three forms, all other forms cannot contain a prime because:

10^n-21, 21*10^n-1, (309*10^n-1)/E, 54*10^n-1, (804*10^n-1)/E

even n: algebra factors (difference of two squares)
odd n: factor of 11

23*10^n-1

even n: factor of 11
odd n: algebra factors (difference of two squares)

(8E4*10^n-1)/E

covering set {5, 11, 25}

also note that the form 1{5}1, which is (14*10^n-41)/E, can be prime only for n=1 because

even n: algebra factors (difference of two squares)
odd n: factor of 11

(and this number for n=1 is exactly 11)

Can someone found a prime of the form {1}55 (111...11155), {2}97 (222...22297), {8}77 (888...88877) in dozenal?

Also {3}11 (333...33311) (3×10^n−201)/E, no known (probable) primes for n>2

[sweety439]

Originally Posted by sweety439

Also {3}11 (333...33311) (3×10^n−201)/E, no known (probable) primes for n>2

Also {1}87 (111...11187) (10^n+6X5)/E

Besides, I found that {3}11 (333...33311) (3×10^n−201)/E cannot be prime since

* For even n, such numbers are divisible by 11
* For odd n, such numbers can be factored as (let n=2*k+1):

((6*10^k-15)/E) * (6*10^k+15)

i.e.

666...6665 * 6000...00015

thus cannot be prime.

[sweety439]

update the file of current status (currently at n=8132)

[sweety439]

done to n=10007, update current status