[EDIT] API since SonarQube v6.3: api / project_analyses / search
[EDIT] Corresponding API for SonarQube LTS v5.6.x: api / projects? versions = true
And since you mention later versions since SonarQube 5.2:
api/ce/component : get pending tasks, execution tasks and the last completed task of this component (usually a project) ( documentation )
PS: api/components/show can be used to get the component identifier from the project keyword
PS2: here is an example of real work in the public project SonarQube . First, get the component ID , then request the component → "submittedAt": "2016-03-07T06:04:31+0100" (a slight difference with the dashboard value due to processing time on the side of the scanner)
Nicolas B. - SonarSource Team
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