2

Click here to load reader

Primal progress: Pattern hunters spy order among prime numbers

Embed Size (px)

Citation preview

Page 1: Primal progress: Pattern hunters spy order among prime numbers

SCIE

NC

E

S C I E N C E N E W S

rials typically used for solar cells, electronsrequire a minimum energy to break freefrom atoms and join an electric current.Most often, electrons get that energy kickfrom solar photons that pack more thanthat minimum energy.

The nanocrystal findings show that theoutcome of the extra energy depends in parton the size of the crystal that absorbs anincoming photon, Klimov says.

Ordinary solar cells are often made fromsemiconductors in the size range of coins orplaying cards. In these cells, the leftoverenergy almost always creates heat via vibra-tions in the semiconductor’s crystal lattice.

Schaller and Klimov worked instead withnanocrystals, about 5 nanometers in diam-eter, of the semiconductor compound leadselenide. They mixed a liquid with the crys-tals, each composed of a few thousandatoms, and sealed a drop in a small glasssheath. The researchers then shot laserpulses at a wide range of photon energiesthrough the sheath to examine thenanocrystals’ responses to light.

When those laser photons carried at leastthree times as much energy as required toknock an electron loose, impact ionizationkicked in, the researchers found. The extraenergy of each photon propelled a liberatedelectron like a cue ball so that it knocked oneand sometimes two additional electronsfree, making them available to join an elec-tric current, Klimov says.

The finding might also open new ways forengineers to improve the performance oflasers and light-emitting diodes made fromnanocrystals, comments Paul Mulvaney ofthe University of Melbourne in Australia.

Because of the large amount of energyneeded to trigger impact ionization in lead-selenide particles and concerns about thetoxicity of lead and selenium, scientists arenow seeking other materials from which tomake the nanocrystals. —P. WEISS

Lava LifeHints of microbes inancient ocean rocks

Samples of lava that erupted onto the oceanfloor almost 3.5 billion years ago containmicroscopic tubes that may have been cre-ated by microbes, researchers say. That sce-nario puts these structures among the old-est known physical remnants of life.

When lava oozes out at midocean ridges

where Earth’s tectonic plates spread apart,water quickly chills the molten material asit moves across the ocean floor. The pastyrock often solidifies into rounded forma-tions dubbed pillow lava. Marine microor-ganisms soon colonize the pillow-lava sur-faces, where they exploit chemical energyto fuel their metabolism (SN: 11/15/03, p. 315). Many studies over the past decadehave found that microbes thrive through-out the uppermost few hundred meters ofthe ocean floor, says Harald Furnes of theUniversity of Bergen in Norway.

Now, analyses of ancient pillow lavas—reported by Furnes and his colleagues inthe April 23 Science—suggest that suchmicrobial colonization has been going onfor billions of years.

Using microscopes, the researchers exam-ined South African rock samples thatformed on an ancient ocean floor between3.48 billion and 3.22 billion years ago. Theoutermost centimeter or so of those pillowlavas is riddled with tubular structures thatrange from 1 to 9 micrometers in diameterand up to 200 µm in length.

The tubular structures, once filled withseawater, are now packed with fine-grainedsilicate minerals. X-ray analyses indicatethat the tubules are lined with carbon, anelement that appears in smaller concentra-tions elsewhere in the rocks. The ratio of theisotopes of carbon-13 and carbon-12 in the

material coating the tubules is lower thanthat normally found in Earth’s crust, a cluethat the substance was produced by—or iswhat’s left of—ancient microorganisms.

Both the presence of the carbon liningand its relative dearth of carbon-13 could beexplained by other phenomena, says TomChacko, a geologist at the University ofAlberta in Edmonton. Together, however,these characteristics—as well as the size andshape of the tubules themselves—stronglysuggest that the features were created andpopulated by ancient microbes. Chackonotes that although previous studies haveidentified lower-than-normal carbon-13concentrations in 3.85-billion-year-old rocksfrom Greenland, suggesting the presence oflife at that time (SN: 11/9/96, p. 292), themore detailed physical evidence describedby Furnes and his colleagues ranks amongthe oldest trace fossils ever reported.

The possibility that signs of ancient life onEarth can persist in rocks for more than 3 billion years makes the find “very excit-ing,” Chacko continues. He notes that someareas of Mars today are littered with vol-canic rocks that may have an underwaterorigin. —S. PERKINS

Primal Progress Pattern hunters spy orderamong prime numbers

Mathematicians have taken a step forwardin understanding patterns within theprimes, numbers divisible only by 1 andthemselves. According to the new work, thepopulation of prime numbers contains aninfinite collection of arithmetic progres-sions—number sequences in which eachterm differs from the preceding one by thesame fixed amount.

For example, in the sequence 3, 5, 7, eachprime number is 2 more than the preced-ing one. Another example of such asequence is 5, 11, 17, 23, 29, in which suc-cessive primes differ by 6.

For centuries, mathematicians have won-dered how many arithmetic progressionssuch as these exist among the set of primenumbers and how long the progressionscan get. In 1939, the Dutch mathematicianJohannes van der Corput proved that thereare infinitely many progressions with threeterms. Whether longer progressions areinfinitely plentiful or limited in number andsize had remained a matter of conjecture.

The longest known progressions havejust 22 terms and lie in remote stretches ofthe number line. For instance, one 22-termprogression starts at 11,410,337,850,553and the difference between successiveterms is 4,609,098,694,200.

Now, a pair of mathematicians offers aproof that in one fell swoop demonstrates

2 6 0 A P R I L 2 4 , 2 0 0 4 V O L . 1 6 5

SCIENCENEWSThis Week

IT’S TUBULAR The cylindrical structures(arrows) riddling this ancient seafloor lavamay have been created by microbes almost3.5 billion years ago. Colors correspond todifferent minerals.

FOBS.4-24 4/21/04 3:05 PM Page 260

Page 2: Primal progress: Pattern hunters spy order among prime numbers

W W W. S C I E N C E N E W S. O R G A P R I L 2 4 , 2 0 0 4 V O L . 1 6 5 2 6 1

that there are infinitely many prime pro-gressions of every finite length. Ben Greenof the University of British Columbia inVancouver and Terence Tao of the Univer-sity of California, Los Angeles report theirfindings in a preprint that they posted onthe Internet on April 8.

It may be months before mathematicianshave finished checking the proof. Never-theless, Green and Tao’s report has sparkedexcitement in the math community.

Proving anything about progressionswith more than three terms had seemedbeyond reach, says Andrew Granville, amathematician at the University of Mon-treal. “If they’ve succeeded in breaking thatbarrier, it’s an extraordinary achievement.”

In their proof, Green and Tao consideredhow the primes relate to a larger set of num-bers that the pair calls almost-primes—numbers that are a product of at most 10primes. Although prime numbers are scarceamong the whole numbers, they are moreplentiful in the narrower setting of thealmost-primes.

Green and Tao showed that the sequenceof almost-primes is pseudorandom;roughly speaking, the almost-primes are“nicely spread out all over the place,” Greensays. The mathematicians then deducedthat the prime numbers are arranged withinthe spread of almost-primes with enoughregularity to ensure that the overallsequence of primes does indeed containarithmetic progressions of every length.

Unfortunately, the new insight about

prime numbers won’t give mathematiciansmuch of a handle on where to look for longprogressions. All it does is guarantee thatfor any length k, there’s a prime progres-sion of that length that starts at a numbersmaller than 2 raised to the power 2 raisedto the power 2 raised to the power 2,repeated k times. But for even small valuesof k, that upper limit quickly becomes astro-nomical.

“The bounds our argument gives areridiculously bad,” Green acknowledges.They are essentially useless, even for math-ematicians with access to the world’s mostpowerful computers, he says.

Green and Tao are now trying to pindown the location of prime arithmetic pro-gressions more precisely. “It’s going to forceus to understand the primes better,” Greensays. —E. KLARREICH

Zapping Wayward CellsTherapy sheds light ontransplant complication

Doctors sometimes recommend ultravio-let (UV) light exposure for people sufferingfrom complications of a bone marrowtransplant from a donor. The radiation canameliorate skin lesions, such as rashes andulcers, that are a common side effect of the

procedure. But UV radiation isn’t a stan-dard treatment, in part because its mech-anism of action is unknown and no large-scale study has established its effectiveness.

An experiment in which mice receivedmarrow transplants now suggests that UVlight wipes out troublemaking immune cellsof the skin. Earlier research had suggestedthat these Langerhans cells react withimmune cells derived from the transplantand cause graft-versus-host disease(GVHD), a dangerous complication inwhich donor immune cells attack the skin,liver, and gut. In the mouse experiment, byhematologist Miriam Merad of the MountSinai School of Medicine in New York andher colleagues at several institutions, UV-light exposure before the transplantationprevented GVHD.

The findings could spur formal trials ofUV therapy in marrow-transplant patients,says Georgia B. Vogelsang, a transplantphysician at Johns Hopkins Medical Insti-tutions in Baltimore.

People typically get bone marrow trans-plants to fight blood cancers, such asleukemia or lymphoma. First, physiciansuse chemotherapy and sometimes gammaor X-ray radiation to kill off fast-dividingcells, such as blood stem cells and bone mar-row cells, which are the source of bothhealthy and cancerous blood cells. Thistreatment wipes out most of the cancer butalso eliminates nearly all of the patient’simmune system.

The patient then receives a donor’s

Transporting drugs into thebody can be hit-or-missbecause many delicate mol-

ecules break down before theyreach their target. In an attemptto develop protective drug-deliv-ery tools, materials scientistshave now fabricated micron-size polymer vesicles that aresturdy enough to navigate thebloodstream unscathed and yetrelease their cargoes on target.

In the past few years, severalresearch groups have focusedon developing drug carrierscalled liposomes (SN: 1/18/03,p. 43). The membranes of thesehollow spheres consist of fattymolecules—lipids—in the samearrangement as that of similarlipids in a living cell’s membrane.However, liposomes themselvesare fragile; their membranes are

“as thin as soap bubbles’,” notesRichard Jones of the Universityof Sheffield in England.

To fabricate tougher lipo-somelike vesicles, TimothyDeming at the University ofCalifornia, Santa Barbara andDarrin Pochan of the Universityof Delaware in Newark enlistedpolymers of amino acids, thebuilding blocks of proteins. Tomake the polymers behave aslipids do, the researchersdesigned the amino acidchains to have one water-repelling and one water-attracting end.

When added to a water solu-tion, these polymers sponta-neously assembled into vesi-cles. However, instead ofhaving two molecule layers, asmembranes of a regular lipo-

some do, the new membraneshad three layers. The addedthickness makes the vesiclestougher than liposomes, theresearchers report in the AprilNature Materials.

“We envision that thesematerials [will] posses attrib-utes useful for applications inbiotechnology and medicine,”say the researchers.

Although thickening thearmor on vesicles can betterprotect their contents, it cre-ates a problem for getting thedrugs out of the vesicles oncue. Deming and his colleaguesovercame that challenge bytweaking the amino acid com-position of the polymer’s water-attracting segment to make thepolymers responsive to achange in acidity, or pH.

The researchers nextenclosed a fluorescent dyeinside vesicles formed from thenew polymer and lowered thepH of the solution containingthe spheres. This disrupted themembranes, releasing the dye.Future alterations in the aminoacids could tailor the vesicles torespond to various pH environ-ments, such as in the gastroin-testinal tract or a cancer cell.

The response to pH is akin tothe way many viruses infectcells, say the researchers. Theacidic cellular interior triggersthe virus’ protein coat to openand release the invader’s genes.

Jones says that vesicles madeof amino acids could be an“altogether more useful prod-uct” for drug delivery than thosemade of liposomes. —A. GOHO

Crafty CarriersArmoring vesicles for more precise and reliable drug delivery

FOBS.4-24 4/21/04 3:06 PM Page 261