Splits the array to parts of equal lengths, len = 3,4,5,...,35 and searches that space for numbers N satisfying N=x(x+1)(x+2)(x+3)(x+4).

reaktor-max.js

var find_greatest = function(input) {
    var check = function(n) {
        if(n==0) { return false; }
        // n is of form x^5 + O(x^4), so we can pick it by taking the
        // fifth root and taking the extra crust off
        var x = Math.floor( Math.pow( n, 0.2 ) ) - 1 
        return n === x*(x+1)*(x+2)*(x+3)*(x+4);
    }

    var slice_n = function(n,x) { 
        return _(_.range(0,Math.ceil(x.length / n))
                    .map(function(i) { 
                        return _.partial(function(b, c, a) { 
                            return a.slice(b, c); 
                        }, n*i, n*i+n);
                    })).map(function(f) { 
                        return f(x) 
                    });
    }

    var check_all = function(x) {
        // find only numbers that are less than 35 digits long 
        var slicers = _.range(3, 36)
            .map(function(n) {
                return _.partial(slice_n, n);
            }),
            makeInt = function(x) { 
                return _(x).map(function(n) { return parseInt(n.replace(/^0*?(\d*)$/, '$1')); });
            };

        return _.filter(
                _.compose(
                    _.uniq, 
                    _.sortBy, 
                    makeInt,
                    _.flatten)(_(slicers).map(function(slicer) { return slicer(x); })), check);
    };

    return _.max(
        check_all(input)
    );
}

find_greatest('144247417057866628561931623430668801207202520672015120302405154409504015444012072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151212312312312312334743784789454578954798451928730302405544095040154441207202520672015120302405544095040154144247299140106872273666980203186723594537960441207202520672015130240554409504015444120720252067201512030240554409504015444120720252067201512030240554409504015444120720252067201512030240554409504015143985091891289122144412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544412072025206720151203024055440950401544400000000000000000000000120720252067201512030240554409504015444014424741705786662856193162343066880')
// 1.4424741705786662e+34
// = 6789245 * 6789246 * 6789247 * 6789248 * 6789249