factordbrpc · fdb
Sign in

Enter a value, an expression, or a term with a variable like 10^n+1 to list a range. Switch to Database id to look a number up by its stored id. Reading never stores anything; use Create to add a number to the database. See the expression syntax & functions reference.

C · No factor known
id #1100000002353913058 290 digits created 2020-12-28

Value

2026754872…29<290>
term (14039^111-1)/11156143511886891090542990102433325233685277658524057702193478413…
Is factor of
SNFS polynomial degree 6 · difficulty 306.9

Special form: 14039^74+14039^37+1. This number divides it, so the number field sieve can use a polynomial with small coefficients. The best one costs about as much as GNFS on a 201-digit number (this number has 290 digits). Listed best first; the files carry sieving parameters for the polynomial's difficulty.

197093521x6 + 14039x3 + 1 difficulty 306.9 · E 3.68e-16 ggnfs msieve cado
197093521x8 + 14039x4 + 1 difficulty 306.9 · E 1.21e-16 ggnfs msieve cado
x6 + 197093521x3 + 38845856020177441 difficulty 323.5 · E 1.69e-17 ggnfs msieve cado
197093521x4 + 14039x2 + 1 difficulty 306.9 · E 4.95e-19 ggnfs msieve cado
15090005…8481<34>x6 + 38845856020177441x3 + 1 difficulty 306.9 · E 2.33e-18 ggnfs msieve cado
x4 + 14039x2 + 197093521 difficulty 315.2 · E 1.31e-19 ggnfs msieve cado
n: 20267548722167359342198528271262394364446793730794012930073702938858701443338397294669966616647008496284249129718603766104317028430976558697861058090351369951232922592789411215018143015661493892115302701382072117835691432122724810415499193624577057392213762569637844289927634136925124436629
# 14039^74+14039^37+1, difficulty: 306.90, scaled difficulty: 306.90
# special-q on the algebraic side, siever gnfs-lasieve4I16e, start at q = 50000000 in ranges of 32000
type: snfs
size: 306
skew: 0.0415
c6: 197093521
c3: 14039
c0: 1
Y1: 1
Y0: -58618417320434524420090958079360449419501482177121
rlim: 100000000
alim: 100000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.6
alambda: 2.6
The block above is a GGNFS / yafu job file for the first polynomial (yafu: save it as nfs.job and resume with -R). The order is for a sieve of this job's size. E is the Murphy score with the conventional fixed parameters, comparable with msieve's; it favours low degrees for small jobs, so it is not always descending.
Trial factoring & ECM effort 11 · TF complete · 2 ECM stages

Work the background scanners have done on this number, from its position in the scanner queue.

Trial division up to 100G
ECM effort P-1 B1=500000 · P+1 c=3 B1=50000 next: ECM c=15 B1=150000

Report factors

Paste anything - plain factors, a GMP-ECM run, a factor list. Every number found is checked for divisibility here; the ones that divide are submitted.

From the command linefdb · curl
fdb
fdb number id:1100000002353913058 --detail 2
curl
curl -s 'https://factordb.com:4059/rpc' -H 'Content-Type: application/json' -d '{"jsonrpc":"2.0","id":1,"method":"get_number","params":{"target":{"id":1100000002353913058},"decimal":false,"detail":2}}'