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C · No factor known
not in database 340 digits

Value

2778472889…01<340>
term 10990^84-10990^77+10990^63-10990^56+10990^42-10990^28+10990^21-10990^7+1
2778472889…01<340> partial
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SNFS polynomial degree 6 · difficulty 339.4

Special form: 10990^84-10990^77+10990^63-10990^56+109…. 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 221-digit number (this number has 340 digits). Listed best first; the files carry sieving parameters for the polynomial's difficulty.

x6 − x5 − 6x4 + 6x3 + 8x2 − 8x + 1 root m = −Y0/Y1 difficulty 339.4 · E 1.17e-16 ggnfs msieve cado
x6 − 19363499…0000<29>x5 + 19363499…9999<29>x4 + x3 − x2 + 19363499…0000<29>x − 19363499…9999<29> difficulty 339.4 · E 1.18e-22 ggnfs msieve cado
10990x8 − 160320279790549900000x7 + 120780100x6 − 17619198…0000<25>x5 + 1327373299000x4 − x3 + 14587832556010000x2 − 10990x + 160320279790549900000 difficulty 359.7 · E 4.84e-22 ggnfs msieve cado
21280485…9010<33>x8 + 19363499…9999<29>x6 + 17619198…0000<25>x4 − 120780100x3 + 160320279790549900000x2 − 10990x + 14587832556010000 difficulty 355.6 · E 4.09e-22 ggnfs msieve cado
x7 − 160320279790549900000x6 + 1327373299000x5 − 21280485…0000<33>x4 + 17619198…0000<25>x3 − 14587832556010000x2 + 23387253…0000<37>x − 19363499…9999<29> difficulty 339.4 · E 3.10e-23 ggnfs msieve cado
14587832556010000x8 − 19363499…0000<29>x7 + 1327373299000x6 − 17619198…0000<25>x5 + 120780100x4 − 21280485…9010<33>x2 − 19363499…9999<29> difficulty 339.4 · E 3.16e-24 ggnfs msieve cado 
n: 2778472889431719398109212324292038778889237615797735406896946894188135204970542104711667205678838443397051928695927076050956770964160605508228122404371140272039682126172539334182552687490332451163821016968555537843753805271661392391643037543259481835200163247188508977408085773671128171280462868296905389389629446559599574869404023010000001
# 10990^84-10990^77+10990^63-10990^56+10990^42-10990^28+10990^21-10990^7+1, difficulty: 339.44, scaled difficulty: 341.60
# special-q on the rational side, siever gnfs-lasieve4I16e, start at q = 50000000 in ranges of 32000
type: snfs
size: 339
skew: 1.1547
c6: 1
c5: -1
c4: -6
c3: 6
c2: 8
c1: -8
c0: 1
Y1: 19363499425130595976990000000
Y0: -374945109987032920875723411770705972609460100000000000001
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.

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From the command linefdb · curl
fdb
fdb number '10990^84-10990^77+10990^63-10990^56+10990^42-10990^28+10990^21-10990^7+1' --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":{"expr":"10990^84-10990^77+10990^63-10990^56+10990^42-10990^28+10990^21-10990^7+1"},"decimal":false,"detail":2}}'