Let's play with 2013 - a numbers game

well, post them, I will do some quality control... also started to get busy in my life again, but I really want to see if this can be done ...

Correction: square((2 squared)!) - 3! + 1 = 571
I'll look at the others later ...

square(((3-1) squared)!) - 2 squared = 572
square((2 squared)!) - 3 = 573
square(((3-1) squared)!) - 2 = 574
square((2 squared)!) - 1 = 575
square((2 squared)!) = 576
square((2 squared)!) + 1 = 577
square(((3-1) squared)!) + 2 = 578
square((2 squared)!) + 3 = 579
square(((3-1) squared)!) + 2 squared = 580
square((2 squared)!) + 3! - 1 = 581
square((2 squared)!) + 3! = 582
square((2 squared)!) + 3! + 1 = 583
square(((3-1) squared)!) + 2 cubed = 584
square((2 squared)!) + 3 squared = 585
square((2 squared)!) + 10 = 586
square((2 squared)!) + summation (3!) - 10 = 587
summation ((2 to the fifth) + 1) + 3 cubed = 588
square((2 squared)!) + 13 = 589

May be I am not reading this right
sum(square(3!) through 2 to the fourth) = 546
so I offer:
((2 squared) ! ) squared) - 30 = 546
============================== =================
Double 2s:
23 squared + (2 squared)! = 553
23 squared + (2 squared) ! + 1 = 554

23 squared + (2 squared)! + 10 = 563
====>
summation (2 to the fifth) + (3! - 1) square = 553
square ((2 squared) ! ) - (sum (3!) + 1) = 554

square ((2 squared) ! ) - 13 = 563
============================== =================
Double 0s:
summation(10 - 3) * 20 = 560
===>
summation ( (2 squared) ! ) - (3-1) to the fourth = 560
============================== =================
One sum too many:
3 cubed * sum(sum(sum(2)!)) = 567
3 cubed * sum(sum(sum(2)!)) + 1 = 568
===>
3 cubed * sum (sum(2) !) ) = 567
3 cubed * sum (sum(2) !) ) + 1 = 568
============================== =================

(sum (sum(2) ) ) ! - 130 = 590

square ( (2 squared) !) + sum (3! - 1) =591
square ( ((3 - 1) squared) ! ) + 2 to the fourth =592
square (square (3! - 1)) - 2 to the fifth = 593
summation (30 + square (2)) - 1 = 594
summation (30 + square (2)) = 595
summation (30 + square (2)) + 1 = 596
square ((2 squared) ! ) + sum (3!) = 597
square ((2 squared) ! ) + sum (3!) + 1 = 598

(3!)! - square of (sum (2 squared) + 1) = 599
3 * 2 * square of 10 = 600

square ( (2 squared)! ) + square (3! - 1) = 601
301 * 2 = 602
201 * 3 = 603
square ( (2 squared)! ) + sum (3! + 1) = 604
(3! - 1) to the fourth - 20 = 605
square ( (2 squared)! ) + 30 = 606
square ( (2 squared)! ) + 31 = 607
square ( (2 squared)! ) + (3-1) to the fifth = 608
(3! - 1) to the fourth - 2 to the fourth = 609
(3!)! - (2 * sum (10)) = 610

sum ( from (sum(2 squared) + 1) to square (3!) ) = 611
2 to the ninth + 10 square = 612
square((2 squared)!) + 10 + 3 cubed = 613
sum ( (3!)! - 1) - 2 to the fourth = 614
2 to the ninth + 10 square + 3 = 615
(2 squared + 1) to fourth - 3 squared = 616
(3! - 1) to the forth - 2 cubed = 617
sum (2 to the fifth) + (3 squared * 10) = 618
(3! - 1) to the forth - sum (sum(2)) = 619
310 * 2 = 620
(3! - 1) to the forth - 2 squared = 621
(2 squared + 1) to fourth - 3 = 622
(3! - 1) to the forth - 2 = 623
sum (sum (2 cubed) - 1) - 3! = 624
(3! - 1) to the forth = 625
sum ( (3!)! - 1) - 2 squared = 626
(3! - 1) to the forth + 2 = 627
(2 squared + 1) to fourth + 3 = 628
(3! - 1) to the forth + 2 squared = 629
sum (sum (2 cubed) - 1) = 630

I think you missed an easy/more eloquent solution fun2come:

21*30 = 630

reverse(summation(20-(1+3)) = 631

I sure did, lol, sometimes I get carried away, so THX !!!
.. and Welcome ...
so we could just reverse some already established numbers .... hmmm, I like the twist and appreciate the novelty in this thread !!!

3! * 10 squared + 2 to the fifth = 632

Need to work on this ... just too much FUN out there recently ...

(3! - 1) to the forth + 2 cubed = 633
(2 squared + 1) to fourth + 3 squared = 634
(3 squared - 2 squared) to the forth + 10 = 635
sum (sum (2 cubed) - 1) + 3! = 636 (iplaypoker, I knew this one would come in handy later)

2 to the ninth + (3! - 1) cubed = 637
sum (3! squared - 1) + 2 cubed = 638
sum (sum (2 cubed) - 1) + 3 squared = 639
2 to the sixth * 10 = 640
(3! - 1) to the fourth + 2 to the fourth = 641
sum ( (3-1) cubed) - (2 squared)! = 642
2 to the sixth * 10 + 3 = 643
(3! squared - 10) squared - 2 to the fifth = 644
(3! - 1) to the fourth + 20 = 645
sum ( (3-1) cubed) - 20 = 646

Now that we had 2013 views of this thread, let me revive it.
.... and be warned, I plan to finish it, even with no more help, yes I am THAT anal when it comes to numbers, but you can always ignore this thread :-)))

Couple of corrections:
sum (sum ( (3-1) cubed)) - (2 squared)! = 642
sum (sum ( (3-1) cubed)) - 20 = 646

Moving ahead:
2 to tenth - summation (3 cubed) + 1 = 647
3 cubed - 3 to the forth = 648
2 to the sixth * 10 + 3 squared = 649
sum (sum ( (3-1) cubed)) - 2 to the fourth = 650

Just had no time or brain to get back to this, so a few easy ones:

reverse (2 to the eight - 10 squared) = 651
reverse (2 to the eight) = 652
reverse (2 to the eighth + 10 squared) = 653
reverse (summation(30) - 2 cubed - 1) = 654
reverse (3 * 10 squared + 2 to the eighth) = 655
summation (3! squared) - 10 = 656
sum ((sum (2)! squared) - 3 squared = 657
sum (3! squared) - 2 cubed = 658
sum ((sum (2)! squared) - 10 + 3 = 659
sum ((sum (2)! squared) - 3! = 660
sum (3! squared) - 2 squared - 1 = 661
sum (3! squared) - 2 squared = 662
sum (3! squared) - 2 - 1 = 663
sum (3! squared) - 2 = 664
sum (3! squared) - 1 = 665
sum (3! squared) = 666
sum (3! squared) + 1 = 667
sum (3! squared) + 2 = 668
sum (3! squared) + 2 + 1 = 669
sum (3! squared) + 2 squared = 670
sum (3! squared) + 2 squared + 1 = 661
sum ((sum (2)! squared) + 3! = 672
sum ((sum (2)! squared) + 10 - 3 = 673
sum (3! squared) + 2 cubed = 674
sum (3! squared) + 2 cubed + 1 = 675
(13 * 2) squared = 676
sum (3! squared) + sum (2 squared) + 1 = 677
sum (3! squared) + 12 =678
sum ((sum (2)! squared) + 13 = 679
(2+3) to the fourth + sum (10) = 680

Games are a bit boring today so far, so let's continue:

reverse ((1+2)! cubed - 30) = 681
reverse (summation of 23 + 10) = 682
reverse (summation (3 cubed) + 2 cubed) = 683
reverse (2*(3 to the fifth)) = 684
reverse (square((2 squared)!) + 10) = 685
summation (3! squared) + 20 = 686
summation (3! squared) + 21 = 687
sum ((sum (2)! squared) + sum (3!) + 1 = 688
summation (3! squared) + (2 squared)! - 1 = 689
summation (3! squared) + (2 squared)! = 690
summation (3! squared) + (2 squared)! +1 = 691
reverse (summation ((2 squared)!) - 3 - 1) = 692
reverse (summation (3 cubed) + 2 cubed + 10) = 693
reverse (summation (31)) = 694
reverse (summation (30 + square (2)) + 1) = 695
sum ((sum (2)! squared) + 30 = 696
sum ((sum (2)! squared) + 31 = 697
summation (3! squared) + 2 to the fifth = 698
summation (3! squared) + 2 to the fifth + 1 = 699
(3!)! -20 = 700

Correction: sum (3! squared) + 2 squared + 1 = 671
which also is exactly the 1/3 mark to 2013

reverse (10 squared + 3 squared - 2) = 701
reverse (summation (20) - 3 ) = 702
reverse (summation ((2 squared)!) + 3! + 1) = 703
reverse (20 squared + 3! + 1) = 704
reverse (2 to the ninth - 3! + 1) = 705
reverse (square ( (2 squared)! ) + 31) = 706
sum (3! squared +1) + 2 squared = 707
(3 to the third -1) squared + 2 to the fifth = 708
sum (3! squared +1) + sum (sum (2)) = 707
3 to the sixth - 20 + 1 = 710
reverse (summation of 3 through (2 to the fourth – 1)) = 711
reverse (summation (20) + 3! + 1) = 712
reverse (summation ((3!-1) squared) - 2 cubed) = 713
reverse (sum(2 to the fifth) - 10 squared - 3 squared) = 714
reverse (2 to the ninth + 3! - 1) = 715
reverse ((3! - 1) to the forth - 2 cubed) = 617
3 to the sixth - 12 = 717
3 to the sixth - sum (2 squared) - 1 = 718
3 to the sixth - 10 = 719
3 to the sixth - (2+1) squared = 720
3 to the sixth - 2 to the third = 721
3 to the sixth - 2 to the third + 1 = 722
3 to the sixth - (2+1)! = 723
3 to the sixth - 2 squared - 1 = 724
3 to the sixth - 2 squared = 725
3 to the sixth - 2 - 1 = 726
3 to the sixth - 2 = 727
3 to the sixth - 1 = 728
3 to the sixth = 729
3 to the sixth + 1 = 730
3 to the sixth + 2 = 731
3 to the sixth + 2 + 1 = 732
3 to the sixth + 2 squared = 733
3 to the sixth + 2 squared + 1 = 734
3 to the sixth + (2+1)! = 735
3 to the sixth + 2 to the third - 1 = 736
3 to the sixth + 2 to the third = 737
3 to the sixth + 2 to the third + 1 = 738
3 to the sixth + 10 = 739
3 to the sixth + sum (2 squared) + 1 = 740
summation (30 + 2 cubed) = 741
summation (30 + 2 cubed) + 1 = 742
reverse ((3! + 1) cubed + 2 squared)) = 743
reverse (21 squared + 3!) = 744
reverse (summation(2 to the fifth) + 10 + 3 squared) = 745
reverse (2 to tenth - summation (3 cubed) + 1) = 746
sum (3! squared) + (2+1) to the forth = 747 (that's a nice airplane) ....