Пентадекатлон мечты

[Dmitriy40]

VAL
Мне даже первое наименьшее дня на 3-4 счёта. Запустил.
Возможно стоит попросить Демиса/DemISdx напрямую.

[VAL]

Dmitriy40 в сообщении #1726755 писал(а):

Запустил.

Спасибо!

Dmitriy40 в сообщении #1726755 писал(а):

Возможно стоит попросить Демиса/DemISdx
напрямую.

Возможно.
Но я почти уверен, что моя просьба и так до него доберется.

[Huz]

VAL
It would really help me if you could show factorizations for the results you report, some of them are very hard for me to reproduce. The related OEIS sequences are unlikely to extend that far, but I'd still like to record them.

(Оффтоп)

For some reason Yandex has stopped working for translation, it just gives a "page not found" error every time. Google loads the page but doesn't translate anything except the top buttons, but still works if I paste individual snippets to its direct translator.

[VAL]

Huz в сообщении #1726760 писал(а):

It would really help me if you could show factorizations for the results you report, some of them are very hard for me to reproduce. The related OEIS sequences are unlikely to extend that far, but I'd still like to record them.

Factorization of which concrete numbers are you interested in?

[VAL]

$M(1400)=7$

38690223912619744665567004493917321974105664865299655586272112666971583294433686851142634866041222350715141173155822015788121657571471921929781245

Все 7 чисел факторизуются без затруднений (All 7 numbers are factorized quickly).

[Huz]

VAL в сообщении #1726763 писал(а):

Huz в сообщении #1726760 писал(а):

It would really help me if you could show factorizations for the results you report, some of them are very hard for me to reproduce. The related OEIS sequences are unlikely to extend that far, but I'd still like to record them.

Factorization of which concrete numbers are you interested in?

I'm currently at $D(680,7)+4 = 11^{16} \cdot 29^4 \cdot 6931223578675161257 \cdot C_{111}$, since my machine crashed a couple of hours in. I haven't yet tried results posted after that.

But of your recently posted results, it already took quite a few hours for me to factor the results before $D(680)$. If it were possible for you to show the factors you have found for each of these results when you post them it would save me quite a bit of time and computer power. (Just a list of prime factors larger than, say, 10-20 digits, excluding the largest factor of each number, would be quite sufficient for my needs - they do not need to be grouped or sorted.)

In particular the Elliptic Curve Method (ECM) relies on randomness, factors it finds easily in one run may not be found at all in another run.

[VAL]

Huz в сообщении #1726781 писал(а):

I'm currently at $D(680,7)+4 = 11^{16} \cdot 29^4 \cdot 6931223578675161257 \cdot C_{111}$, since my machine crashed a couple of hours in. I haven't yet tried results posted after that.

n+4 = 11^16 × 29^4 × 6 931223 578675 161257 × 2 025470 216583 812520 605299 × 
        128 000903 620463 594136 005171 998632 870293 696106 563729 935417 522220 997868 360573 534340 917523 (87 digits)

  n+6 = 3^16 × 41^4 × 928177 × 1 968868 493917 466020 248827 × 
        262724 603264 730379 447854 613309 582194 949421 316696 660296 494255 758229 651059 067771 495157 209070 561553 924314 896649 (108 digits)

[VAL]

$M(1088)=7$

n = 964079833874499989281038932959228395991253674489512126503298135028479152854509665927880850033654663231331256563424415982519836425781245 

n+4 = 7^16 × 179 × 1783 × 78 654703 792321 × 3243 343481 833757 × 6 191945 164525 640682 604901 × 57 543362 808408 099352 957028 651083 032298 740122 946159 452361 547181 (62 digits)

n+6 = 3^16 × 109321 × 12 355729 × 787 366792 417649 × 2 359084 531059 198211 × 466219 880783 725484 728111 × 188730 058108 298837 438652 346228 520909 038960 847358 586255 523671 (60 digits)

[Huz]

VAL, thank you.

(The result for $n_{1088}+6$ is for a different number, the correct factorization has 382911534452111716427921 as the important factor.)

[Dmitriy40]

VAL

n+6 = 3^16 × 1423 × 2137 × 3803 × 382911 534452 111716 427921 × 32098 608222 972828 211583 757680 737537 (35 digits) × 157562 377210 001873 047380 986695 510699 976839 221060 027960 309151 (60 digits)

[VAL]

Huz в сообщении #1726805 писал(а):

(The result for $n_{1088}+6$ is for a different number, the correct factorization has 382911534452111716427921 as the important factor.)

I don't know where I copied my "factorization" from. Dmitry gave the correct version.

[VAL]

$M(4000)=7$

n = 12771 919017 941713 225582 762329 303870 947376 325406 283429 005811 418117 586148 768956 745104 845143 793987 362047 755411 960564 304363 982019 346743 664414 301652 139007 541245 (155 digits)

n + 6 = 3^4 × 17^4 × 19^4 × 833689 × 269 383428 162323 × 5251 420307 083681 × 17 736991 440695 625600 865709 × 692 515288 346237 599725 846749 344547 359920 471732 119993 398076 149136 252382 449186 911037 (81 digits)

[Huz]

This was unexpected, after 440 CPU days found a new lower bound for D(48,10) ten times smaller than the previous one (243601189639274971), with surprisingly high primes in the squares:

D(48,10) <= 22911293821947932:
n+0 = 2^2 . 73.197.3251.122513393
n+1 = 647^2 . 3.19.1489.644869
n+2 = 13^2 . 2.1277.128153.414203
n+3 = 67^2 . 5.31.887.37123139
n+4 = 2^5 . 3.1327043.179842937
n+5 = 7^2 . 257.349.12263.425107
n+6 = 11^2 . 2.277.4093.83505049
n+7 = 3^2 . 53.59.1993.408481061
n+8 = 2^2 . 5.109.139.75609840347
n+9 = 29^2 . 241.307.13499.27277

[EUgeneUS]

Huz в сообщении #1726882 писал(а):

after 440 CPU days found a new lower bound for D(48,10) ten times smaller than the previous one

Congratulations!

Huz в сообщении #1726882 писал(а):

... with surprisingly high primes in the squares:

I don't find that surprising.
I am almost certain that the lower bound estimates obtained using patterns involving the substitution of small primes into squares could be improved by roughly an order of magnitude—or even more—if substitutions of relatively large primes were used.

[Yadryara]

Congrat, Hugo!