First there was a computerized inventory of 301,000 fragments, some as small as an inch. Next came 450,000 high-quality photographs, on blue backgrounds to highlight visual cues, and a Web site where researchers can browse, compare, and consult thousands of bibliographic citations of published material.

The latest experiment involves more than 100 linked computers located in a basement room at Tel Aviv University here, cooled by standup fans. They are analyzing 500 visual cues for each of 157,514 fragments, to check a total of 12,405,251,341 possible pairings. The process began May 16 and should be done around June 25, according to an estimate on the project’s Web site.

Yaacov Choueka, a retired professor of computer science who runs the Friedberg-financed Genazim project in Jerusalem, said the goals are not only to democratize access to the documents and speed up the elusive challenge of joining fragments, but to harness the computer’s ability to pose new research questions.

“Which is really what computers should do, not just process salaries and monitor traffic,” said Professor Choueka, who was a leader of the team at Bar-Ilan University that developed the Responsa Project, an electronic collection of questions and answers about Jewish law that won a prestigious Israel Prize in 2007.

“I want from the computer to give me something new, a new horizon, a new tool that was never there before.”

Another developing technology is a “jigsaw puzzle” feature, with touch-screen technology that lets users enlarge, turn and skew fragments to see if they fit together. Professor Choueka, who was born in Cairo in 1936, imagines that someday soon such screens will be available alongside every genizah collection. And why not a genizah-jigsaw app for smartphones?

“The thing it really makes possible is people from all walks of life, in academia and out, to look at unpublished material,” said Ben Outhwaite, head of the Genizah Research Unit at Cambridge University, home to 60 percent of the fragments. “No longer are we going to see a few great scholarly names hoarding particular parts of the genizah and have to wait 20 years for their definitive publication. Now everyone can dive in.”