Let's play with 2013 - a numbers game

summation (3 cubed) - 2 cubed + 1 = 371
summation (3 cubed) - (2 + 1)! = 372
summation (3 cubed) - 2 squared - 1 = 373
summation (3 cubed) - 2 squared = 374
summation (3 cubed) - 1 - 2 = 375
summation (3 cubed) - 2 = 376
summation (3 cubed) - 1 = 377
summation (3 cubed) = 378
summation (3 cubed) + 1 = 379
summation (3 cubed) + 2 = 380
summation (3 cubed) + 2 + 1 = 381
summation (3 cubed) + 2 squared = 382
summation (3 cubed) + 2 squared + 1 = 383
summation (3 cubed) + (2 + 1)! = 384
summation (3 cubed) + 2 cubed - 1 = 385
summation (3 cubed) + 2 cubed = 386
summation (3 cubed) + 2 cubed + 1 = 387
summation (3 cubed) + 10 = 388
(3 squared + 2 cubed) squared + 10 squared = 389
summation (3 cubed) + 12 = 390

Okay, I've done my contribution for the day. I'm ready to play.
10 squared * 2 squared - 3 squared = 391
summation (3 cubed) + 2 squared + 10 = 392
summation (3 cubed) + 2 to the fourth - 1 = 393
summation (3 cubed) + 2 to the fourth = 394
summation (3 cubed) + 2 to the fourth + 1 = 395
summation (3 cubed) + 2 cubed + 10 = 396
10 squared * 2 squared - 3 = 397
summation (3 cubed) + 2 *10 = 398
20 squared - 1 = 399
10 squared * 2 squared = 400
summation (3 cubed) + (2 squared)! - 1 = 401
summation (3 cubed) + (2 squared)! = 402
10 squared * 2 squared + 3 = 403
summation ((3 cubed) +1) - 2 = 404
summation (3 cubed) + (2 + 1) cubed = 405
summation ((3 cubed) +1) = 406
20 squared + 3! + 1 = 407
summation ((3 cubed) +1) + 2 = 408
10 squared * 2 squared + 3 squared = 409
summation (3 cubed) + 2 to the fifth = 410

:-) will check you later

21 squared - 30 = 411

The next 16:

103 * 2 squared = 412
20 squared + 13 = 413 (almost looks like 2013!)
summation ((3 cubed) +1) + 2 cubed = 414
summation (3 cubed) + summation (2 cubed) + 1 = 415
13 * 2 to the fifth = 416
sum(2 to the fifth) - 10 squared - 3 squared = 417
sum(3 cubed) + (2 squared * 10) = 418
sum(30 - 1) - 2 to the fourth = 419
(3!)! - sum((2 squared)!) = 420
(3!)! - sum((2 squared)!) + 1 = 421
sum(sum(3!+1)) + 2 to the fourth = 422
(sum(3 squared) + 2) * (10 - 1) = 423
20 squared + (3 + 1)! = 424
sum((3+2)squared) + 10 squared = 425
summation ((3 cubed) +1) + 20 = 426
sum(30 - 1) - 2 cubed = 427

I think we need to redo 423
sum (3 cubed) + sum ((2+1) squared) = 423

20 squared + sum (3! +1) = 428

I think we need to redo 423
sum (3 cubed) + sum ((2+1) squared) = 423

20 squared + sum (3! +1) = 428 Originally Posted by fun2come

Now I see. Another duplicate one slipped through my quality control.

sum(30) - sum(2 cubed) = 429
sum(30) - sum(2 cubed) + 1 = 430
20 squared + 31 = 431
20 squared + (3 - 1) to the fifth = 432
sum (3 cubed) + sum(10) = 433
sum (3 cubed) + sum(sum(2 squared)) + 1 = 434
sum(30 - 1) = 435
3 * (10 squared) + sum(2 to the fourth) = 436
summation (30 - 1) + 2 = 437
21 squared - 3 = 438
summation (30 - 1) + 2 squared = 439
((sum(3!)) squared) - 1 = 440
21 squared = 441
((sum(3!)) squared) + 1 = 442
((sum(3!)) squared) + 2 = 443
21 squared + 3 = 444

20 squared + summation (3 squared) = 445
20 squared + summation (3 squared) + 1 = 446
21 squared + 3! = 447
(3! + 1) * 2 to the sixth = 448
((sum(3!)) squared) + 2 cubed = 449
summation (3 squared) * 10 = 450
((sum(3!)) squared) + 10 = 451

A little trivia: this group includes two pairs of sexy primes: 457 and 463, and 461 and 467. A sexy prime is a member of a pair of prime numbers separated by 6. In this case we have two pairs co-mingled, so maybe they are having group sex.

Also, if p+2 or p+4 is prime, they are considered prime triplets, like 461, 463, and 467. Menage aux trois, anyone? At the very least, maybe a little love triangle.

Ahh, the secret life of numbers. And, yes, I've been checking some of the numbers on Wikipedia, because they're getting a little large to factor otherwise.

sum(3 squared) * 10 + 2 = 452
summation(30) - 12 = 453
sum(3 squared) * 10 + 2 squared = 454
summation(30) - summation(2 squared) = 455
summation(30) - 2 cubed - 1 = 456
summation(30) - 2 cubed = 457
summation(30) - 2 cubed + 1 = 458
summation(30) - (summation of 2)! = 459
summation(30) - 2 squared - 1 = 460
summation (30) - 2 squared = 461
summation(30) - 2 - 1 = 462
summation(30) - 2 = 463
summation(30) - 1 = 464
summation(30) = 465
summation(30) + 1 = 466
summation(30) + 2 = 467

NICE, and THX for the easy pass, so I can do a few real easy ones:

summation(30) + 2 + 1 = 468
summation(30) + 2 squared = 469
summation(30) + 2 squared + 1 = 470
summation(30) + (summation of 2)! = 471
summation(30) + 2 cubed - 1 = 472
summation(30) + 2 cubed = 473
summation(30) + 2 cubed + 1 = 474
summation(30) + summation(2 squared) = 475
summation(31) - 20 = 476

summation(30) + 12 = 477
summation(3 cubed) + 10 squared = 478
summation(3 cubed - 1) + 2 to the seventh = 479
summation(31) - 2 to the fourth = 480
20 squared + 3 to the fourth = 481
20 squared + 3 to the fourth + 1 = 482
summation(2 to the fifth) - summation(3 squared) = 483
summation(2 to the fifth) - summation(3 squared) + 1 = 484
2*(3 to the fifth) - 1 = 485
2*(3 to the fifth) = 486
2*(3 to the fifth) + 1 = 487
2 to the ninth - (3 + 1)! = 488
summation(30) + (2 squared)! = 489
square(2 squared + 3) * 10 = 490
20 squared + summation of 13 = 491
summation(30) + (2 + 1) cubed = 492

summation (10) * 3 squared - 2 = 493
summation (31) - 2 = 494
summation (10) * 3 squared = 495
summation (31) = 496
summation (10) * 3 squared + 2 = 497
summation (31) + 2 = 498
summation (10) * 3 squared + 2 squared = 499
summation (31) + 2 squared = 500

WOW 500....

Easy ones, except the first:

summation (2 to the fifth) - 3 cubed = 501
2 to the ninth - 10 = 502
2 to the ninth - 3 squared = 503
2 to the ninth - (3-1)cubed = 504
2 to the ninth - 3! - 1 = 505
2 to the ninth - 3! = 506
2 to the ninth - 3! + 1 = 507
2 to the ninth - (3-1)squared = 508
2 to the ninth - 3 = 509
2 to the ninth - 3 + 1 = 510
2 to the ninth - 1 = 511
2 to the ninth = 512
2 to the ninth + 1 = 513
2 to the ninth + 3 - 1 = 514
2 to the ninth + 3 = 515
2 to the ninth + (3-1)squared = 516
2 to the ninth + 3! - 1 = 517
2 to the ninth + 3! = 518
2 to the ninth + 3! + 1 = 519
2 to the ninth + (3-1)cubed = 520
2 to the ninth + 3 squared = 521
2 to the ninth + 10 = 522

summation (2 to the fifth) - 3! + 1 = 523
summation (2 to the fifth) - 3 - 1 = 524
summation (2 to the fifth) - 3 = 525
summation (2 to the fifth) - 3 + 1 = 526
summation (2 to the fifth) - 1 = 527
summation (2 to the fifth) = 528
23 squared = 529
23 squared + 1 = 530
summation (2 to the fifth) + 3 = 531
summation (2 to the fifth) + 3 + 1 = 532
summation (2 to the fifth) + 3! - 1 = 533
summation (2 to the fifth) + 3! = 534
summation (2 to the fifth) + 3! + 1 = 535
summation (2 to the fifth) + (3 - 1) cubed = 536
summation (2 to the fifth) + 3 squared = 537
summation (2 to the fifth) + 10 = 538
23 squared + 10 = 539
2 to the ninth + summation(3! + 1) = 540
summation (2 to the fifth) + 13 = 541

No fun playing alone .... I'll wait for somebody to continue, even though I have more numbers to offer :-)

( (3!) to the third + Summation (10) ) * 2 = 542

So sorry, my friend, for leaving you feeling alone and abandoned. Life circumstances. Nothing personal, rest assured.

So how far along are you? I'm at 833, but they all need checking. Lots of sins along the way.

2 to the ninth + 30 = 542
2 to the ninth + 31 = 543
((2 squared)! + 1) squared - 3 to the fourth = 544
square of (2 squared)! - 31 = 545
sum(square(3!) through 2 to the fourth) = 546
summation(2 to the fifth) + 10 + 3 squared = 547
2 to the ninth + 3! squared = 548
2 to the ninth + 3 cubed + 10 =549
sum(sum(2 squared) * 10 = 550
(summation(3 cubed + sum(summation of 2) - 10 = 551
summation(2 to the fifth + 1) - 3 squared = 552
23 squared + (2 squared)! = 553
23 squared + (2 squared) ! + 1 = 554
square ((2 squared)!) - summation of 3! = 555
3 * 10 squared + 2 to the eighth = 556
summation(2 to the fifth) + 30 - 1 = 557
summation(2 to the fifth) + 30 = 558
summation(2 to the fifth) + 30 + 1 = 559
summation(10 - 3) * 20 = 560
summation(32 + 1) = 561
sum(3 cubed + sum(sum(2))) + 1 = 562
23 squared + (2 squared)! + 10 = 563
summation(2 to the fifth + 1) + 3 = 564
square ((2 squared)!) - summation of 3! + 10 =565
2 to the eight + 310 = 566
3 cubed * sum(sum(sum(2)!)) = 567
3 cubed * sum(sum(sum(2)!)) + 1 = 568
square((2 squared)!) - 3! - 1 = 569
square((2 squared)!) - 3! = 570
square((2 squared)!) - 3! - 1 = 571