Skip to content
2000
Volume 32, Issue 9
  • ISSN: 0929-8673
  • E-ISSN: 1875-533X

Abstract

Turmerones are major bioactive compounds of species with several beneficial pharmacological activities. In addition, various and studies noted that turmerones could affect different cytokines, metabolic pathways, and targets. Turmerones will have the potential to be a candidate agent to lessen many pathological and immunological conditions as a result of these pharmacological activities. In this review, we provided information about the pharmacological actions of turmerones using search engines such as PubMed, Google Scholar, Scopus, and Web of Science.

Loading

Article metrics loading...

/content/journals/cmc/10.2174/0929867331666230907112441
2023-10-09
2025-04-12
Loading full text...

Full text loading...

References

  1. VaughnA.R. BranumA. SivamaniR.K. Effects of turmeric (Curcuma longa) on skin health: A systematic review of the clinical evidence.Phytother. Res.20163081243126410.1002/ptr.564027213821
    [Google Scholar]
  2. KocaadamB. ŞanlierN. Curcumin, an active component of turmeric (Curcuma longa), and its effects on health.Crit. Rev. Food Sci. Nutr.201757132889289510.1080/10408398.2015.107719526528921
    [Google Scholar]
  3. KhayatanD. RazaviS.M. ArabZ.N. NiknejadA.H. NouriK. MomtazS. GumprichtE. JamialahmadiT. AbdolghaffariA.H. BarretoG.E. SahebkarA. Protective effects of curcumin against traumatic brain injury.Biomed. Pharmacother.202215411362110.1016/j.biopha.2022.11362136055110
    [Google Scholar]
  4. AhsanR. ArshadM. KhushtarM. AhmadM.A. MuazzamM. AkhterM.S. GuptaG. MuzahidM. A comprehensive review on physiological effects of curcumin.Drug Res.2020701044144710.1055/a‑1207‑946932746480
    [Google Scholar]
  5. Keihanian, F.; Saeidinia, A.; Bagheri, R.K.; Johnston, T.P.; Sahebkar, A.; Curcumin, hemostasis, thrombosis, and coagulation. J. Cell Physiol., 2018, 233(6), 4497-4511.10.1002/jcp.26249
  6. GanjiA. FarahaniI. SaeedifarA.M. MosayebiG. GhazaviA. MajeedM. JamialahmadiT. SahebkarA. Protective effects of curcumin against lipopolysaccharide-induced toxicity.Curr. Med. Chem.202128336915693010.2174/092986732866621052512470734036908
    [Google Scholar]
  7. HasanzadehS. ReadM.I. BlandA.R. MajeedM. JamialahmadiT. SahebkarA. Curcumin: An inflammasome silencer.Pharmacol. Res.202015910492110.1016/j.phrs.2020.10492132464325
    [Google Scholar]
  8. Marjaneh, R.M.; Rahmani, F.; Hassanian, S.M.; Rezaei, N.; Hashemzehi, M.; Bahrami, A.; Ariakia, F.; Fiuji, H.; Sahebkar, A.; Avan, A.; Khazaei, M. Phytosomal curcumin inhibits tumor growth in colitis-associated colorectal cancer. J. Cell. Physiol. 2018; 233(10), 6785-6798.10.1002/jcp.26538
  9. NairA. AmalrajA. JacobJ. KunnumakkaraA.B. GopiS. Non-curcuminoids from turmeric and their potential in cancer therapy and anticancer drug delivery formulations.Biomolecules2019911310.3390/biom901001330609771
    [Google Scholar]
  10. DosokyN. SetzerW. Chemical composition and biological activities of essential oils of Curcuma species.Nutrients2018109119610.3390/nu1009119630200410
    [Google Scholar]
  11. JayaprakashaG.K. JenaB.S. NegiP.S. SakariahK.K. Evaluation of antioxidant activities and antimutagenicity of turmeric oil: A byproduct from curcumin production.Z. Naturforsch. C J. Biosci.2002579-1082883510.1515/znc‑2002‑9‑101312440720
    [Google Scholar]
  12. LekshmiP.C. ArimboorR. IndulekhaP.S. Nirmala MenonA. Turmeric (Curcuma longa L.) volatile oil inhibits key enzymes linked to type 2 diabetes.Int. J. Food Sci. Nutr.201263783283410.3109/09637486.2011.60715622385048
    [Google Scholar]
  13. HucklenbroichJ. KleinR. NeumaierB. GrafR. FinkG.R. SchroeterM. RuegerM.A. Aromatic-turmerone induces neural stem cell proliferation in vitro and in vivo.Stem Cell Res. Ther.20145410010.1186/scrt50025928248
    [Google Scholar]
  14. Mohammed, E.S.; El-Beih, N.M.; El-Hussieny, E.A.; El-Ahwany, E.; Hassan, M., Zoheiry, M.; Effects of free and nanoparticulate curcumin on chemically induced liver carcinoma in an animal model. Arch. Med. Sci. : AMS, 2020 17(1), 218–227.10.5114/aoms.2020.93739
  15. AnandP. KunnumakkaraA.B. NewmanR.A. AggarwalB.B. Bioavailability of curcumin: Problems and promises.Mol. Pharm.20074680781810.1021/mp700113r17999464
    [Google Scholar]
  16. GuptaS.C. PatchvaS. AggarwalB.B. Therapeutic roles of curcumin: Lessons learned from clinical trials.AAPS J.201315119521810.1208/s12248‑012‑9432‑823143785
    [Google Scholar]
  17. Cicero, A.F.G.; Sahebkar, A.; Fogacci, F.; Bove, M.; Giovannini, M.; Borghi, C.; Effects of phytosomal curcumin on anthropometric parameters, insulin resistance, cortisolemia and non-alcoholic fatty liver disease indices: A double-blind, placebo-controlled clinical trial. Europ. J. Nutr., 2020, 59(2), 477–483.10.1007/s00394‑019‑01916‑7
  18. Iranshahi, M.; Sahebkar, A.; Hosseini, S. T.; Takasaki, M.; Konoshima, T.; Tokuda, H.; Cancer chemopreventive activity of diversin from Ferula diversivittata in vitro and in vivo. Phytomedicine, 2010, 17(3-4), 269–273.10.1016/j.phymed.2009.05.020
  19. MohajeriM. SahebkarA. Protective effects of curcumin against doxorubicin-induced toxicity and resistance: A review.Crit. Rev. Oncol. Hematol.2018122305110.1016/j.critrevonc.2017.12.00529458788
    [Google Scholar]
  20. Mokhtari-ZaerA. MarefatiN. AtkinS.L. ButlerA.E. SahebkarA. The protective role of curcumin in myocardial ischemia–reperfusion injury.J. Cell. Physiol.2019234121422210.1002/jcp.2684829968913
    [Google Scholar]
  21. Mohammadi, A.; Blesso, C.N.; Barreto, G.E.; Banach, M.; Majeed, M.; Sahebkar, A. Macrophage plasticity, polarization and function in response to curcumin, a diet-derived polyphenol, as an immunomodulatory agent. J. Nutri. Biochem., 2019, 66, 1–16. 10.1016/j.jnutbio.2018.12.005
  22. Panahi, Y.; Fazlolahzadeh, O.; Atkin, S.L.; Majeed, M.; Butler, A.E.; Johnston, T.P.; Sahebkar, A.; Evidence of curcumin and curcumin analogue effects in skin diseases: A narrative review. J. Cell. Physiol., 2019, 234(2), 1165–1178.10.1002/jcp.27096
  23. Panahi, Y.; Sahebkar, A.; Amiri, M.; Davoudi, S.M.; Beiraghdar, F.; Hoseininejad, S.L.; Kolivand, M.; Improvement of sulphur mustard-induced chronic pruritus, quality of life and antioxidant status by curcumin: Results of a randomised, double-blind, placebo-controlled trial. Br. J. Nutri., 2012, 108(7), 1272–1279.10.1017/S0007114511006544
  24. JiM. ChoiJ. LeeJ. LeeY. Induction of apoptosis by ar-turmerone on various cell lines.Int. J. Mol. Med.200414225325610.3892/ijmm.14.2.25315254774
    [Google Scholar]
  25. AraújoC.A.C. LeonL.L. Biological activities of Curcuma longa L.Mem. Inst. Oswaldo Cruz200196572372810.1590/S0074‑0276200100050002611500779
    [Google Scholar]
  26. ObulesuM. Health benefits of turmeric: Emphasis on anticancer activity.Turmeric and Curcumin for Neurodegenerative Diseases202131810.1016/B978‑0‑12‑822448‑9.00006‑6
    [Google Scholar]
  27. YueG.G.L. ChanB.C.L. HonP.M. LeeM.Y.H. FungK.P. LeungP.C. LauC.B.S. Evaluation of in vitro anti-proliferative and immunomodulatory activities of compounds isolated from Curcuma longa.Food Chem. Toxicol.2010488-92011202010.1016/j.fct.2010.04.03920438793
    [Google Scholar]
  28. YueG.G.L. ChengS.W. YuH. XuZ.S. LeeJ.K.M. HonP.M. LeeM.Y.H. KennellyE.J. DengG. YeungS.K. CassilethB.R. FungK.P. LeungP.C. LauC.B.S. The role of turmerones on curcumin transportation and P-glycoprotein activities in intestinal Caco-2 cells.J. Med. Food201215324225210.1089/jmf.2011.184522181075
    [Google Scholar]
  29. SagaY. HatakenakaY. MatsumotoM. YoshiokaY. MatsumuraS. ZaimaN. KonishiY. Neuroprotective effects of aromatic turmerone on activity deprivation-induced apoptosis in cerebellar granule neurons.Neuroreport202031181302130710.1097/WNR.000000000000155133165195
    [Google Scholar]
  30. HoriY. TsutsumiR. NasuK. BoatengA. AshikariY. SugiuraM. NakajimaM. KurauchiY. HisatsuneA. KatsukiH. SekiT. Aromatic-turmerone analogs protect dopaminergic neurons in midbrain slice cultures through their neuroprotective activities.Cells.2021105109010.3390/cells1005109034063571
    [Google Scholar]
  31. ChenM. ChangY.Y. HuangS. XiaoL.H. ZhouW. ZhangL.Y. LiC. ZhouR.P. TangJ. LinL. DuZ.Y. ZhangK. Aromatic-turmerone attenuates lps-induced neuroinflammation and consequent memory impairment by targeting TLR4-Dependent signaling pathway.Mol. Nutr. Food Res.201862228849618
    [Google Scholar]
  32. PoserS.W. Androutsellis-TheotokisA. Spicing up endogenous neural stem cells: aromatic-turmerone offers new possibilities for tackling neurodegeneration.Stem Cell Res. Ther.20145612710.1186/scrt51725688994
    [Google Scholar]
  33. TiwariS. AtluriV. KaushikA. YndartA. NairM. Alzheimer’s disease: Pathogenesis, diagnostics, and therapeutics.Int. J. Nanomedicine2019145541555410.2147/IJN.S20049031410002
    [Google Scholar]
  34. IwamotoK. MatsumuraS. YoshiokaY. YamamotoA. MakinoS. MoriyamaT. ZaimaN. Using turmeric oil as a solvent improves the distribution of sesamin-sesamolin in the serum and brain of mice.Lipids.201954531132010.1002/lipd.1214730993746
    [Google Scholar]
  35. ParkS.Y. JinM.L. KimY.H. KimY. LeeS.J. Anti-inflammatory effects of aromatic-turmerone through blocking of NF-κB, JNK, and p38 MAPK signaling pathways in amyloid β-stimulated microglia.Int. Immunopharmacol.2012141132010.1016/j.intimp.2012.06.00322728094
    [Google Scholar]
  36. Orellana-PaucarA.M. AfrikanovaT. ThomasJ. AibuldinovY.K. DehaenW. de WitteP.A.M. EsguerraC.V. Insights from zebrafish and mouse models on the activity and safety of ar-turmerone as a potential drug candidate for the treatment of epilepsy.PLoS One2013812e8163410.1371/journal.pone.008163424349101
    [Google Scholar]
  37. ParkS.Y. KimY.H. KimY. LeeS.J. Aromatic-turmerone’s anti-inflammatory effects in microglial cells are mediated by protein kinase A and heme oxygenase-1 signaling.Neurochem. Int.201261576777710.1016/j.neuint.2012.06.02022766494
    [Google Scholar]
  38. LiY.L. DuZ.Y. LiP.H. YanL. ZhouW. TangY.D. LiuG.R. FangY.X. ZhangK. DongC.Z. ChenH.X. Aromatic-turmerone ameliorates imiquimod-induced psoriasis-like inflammation of BALB/c mice.Int. Immunopharmacol.20186431932510.1016/j.intimp.2018.09.01530243067
    [Google Scholar]
  39. YangS. LiuJ. JiaoJ. JiaoL. Ar-turmerone exerts anti-proliferative and anti-inflammatory activities in HaCaT keratinocytes by inactivating hedgehog pathway.Inflammation.202043247848610.1007/s10753‑019‑01131‑w31773440
    [Google Scholar]
  40. OhS. HanA.R. ParkH.R. JangE.J. KimH.K. JeongM.G. SongH. ParkG.H. SeoE.K. HwangE.S. Suppression of inflammatory cytokine production by ar-turmerone isolated from curcuma phaeocaulis.Chem. Biodivers.20141171034104110.1002/cbdv.20130039725044589
    [Google Scholar]
  41. LiC. ZhangW. WuX. CaiQ. TanZ. HongZ. HuangS. YuanY. YaoL. ZhangL. Aromatic- turmerone ameliorates DSS-induced ulcerative colitis via modulating gut microbiota in mice.Inflammopharmacology.20223041283129410.1007/s10787‑022‑01007‑w35794287
    [Google Scholar]
  42. GadnayakA. DehuryB. NayakA. JenaS. SahooA. PandaP.C. RayA. NayakS. Mechanistic insights into 5-lipoxygenase inhibition by active principles derived from essential oils of Curcuma species: Molecular docking, ADMET analysis and molecular dynamic simulation study.PLoS One.2022177e027195610.1371/journal.pone.027195635867724
    [Google Scholar]
  43. PricciM. GirardiB. GiorgioF. LosurdoG. IerardiE. Di LeoA. Curcumin and colorectal cancer: From basic to clinical evidences.Int. J. Mol. Sci.2020217236410.3390/ijms2107236432235371
    [Google Scholar]
  44. YueG.G.L. KwokH.F. LeeJ.K.M. JiangL. WongE.C.W. GaoS. WongH.L. LiL. ChanK.M. LeungP.C. FungK.P. ZuoZ. LauC.B.S. Combined therapy using bevacizumab and turmeric ethanolic extract (with absorbable curcumin) exhibited beneficial efficacy in colon cancer mice.Pharmacol. Res.2016111435710.1016/j.phrs.2016.05.02527241019
    [Google Scholar]
  45. LiM. YueG.G.L. TsuiS.K.W. FungK.P. LauC.B.S. Turmeric extract, with absorbable curcumin, has potent anti-metastatic effect in vitro and in vivo.Phytomedicine20184613114110.1016/j.phymed.2018.03.06530097113
    [Google Scholar]
  46. RouhollahiE. ZorofchianM.S. PaydarM. FadaeinasabM. ZahedifardM. HajrezaieM. AbdallaA.H.O. Yeng LooiC. AmeenA.M. AwangK. MohamedZ. Inhibitory effect of Curcuma purpurascens BI. rhizome on HT-29 colon cancer cells through mitochondrial-dependent apoptosis pathway.BMC Complement. Altern. Med.20151511510.1186/s12906‑015‑0534‑625652758
    [Google Scholar]
  47. KarimianH. AryaA. FadaeinasabM. RazaviM. HajrezaeiM. Karim KhanA. Mohd AliH. AbdullaM.A. NoordinM.I. Kelussia odoratissima Mozaff. activates intrinsic pathway of apoptosis in breast cancer cells associated with S phase cell cycle arrest via involvement of p21/p27 in vitro and in vivo.Drug Des. Devel. Ther.20171133735010.2147/DDDT.S12151828203057
    [Google Scholar]
  48. AratanechemugeY. KomiyaT. MotekiH. KatsuzakiH. ImaiK. HibasamiH. Selective induction of apoptosis by ar-turmerone isolated from turmeric (Curcuma longa L)in two human leukemia cell lines, but not in human stomach cancer cell line.Int. J. Mol. Med.20029548148410.3892/ijmm.9.5.48111956652
    [Google Scholar]
  49. LeeY.K. Activation of apoptotic protein in U937 cells by a component of turmeric oil.BMB Rep.20094229610010.5483/BMBRep.2009.42.2.09619250610
    [Google Scholar]
  50. ChengS.B. WuL.C. HsiehY.C. WuC.H. ChanY.J. ChangL.H. ChangC.M.J. HsuS.L. TengC.L. WuC.C. Supercritical carbon dioxide extraction of aromatic turmerone from Curcuma longa Linn. induces apoptosis through reactive oxygen species-triggered intrinsic and extrinsic pathways in human hepatocellular carcinoma HepG2 cells.J. Agric. Food Chem.201260389620963010.1021/jf301882b22946656
    [Google Scholar]
  51. ParkS.Y. KimY.H. KimY. LeeS.J. Aromatic-turmerone attenuates invasion and expression of MMP-9 and COX-2 through inhibition of NF-κB activation in TPA-induced breast cancer cells.J. Cell. Biochem.2012113123653366210.1002/jcb.2423822740037
    [Google Scholar]
  52. NatrajanD. SrinivasanS. SundarK. RavindranA. Formulation of essential oil-loaded chitosan-alginate nanocapsules.Yao Wu Shi Pin Fen Xi201523356056828911716
    [Google Scholar]
  53. ParkS.Y. JinM.L. KimY.H. KimY. LeeS.J. Aromatic-turmerone inhibits α-MSH and IBMX-induced melanogenesis by inactivating CREB and MITF signaling pathways.Arch. Dermatol. Res.20113031073774410.1007/s00403‑011‑1155‑721660443
    [Google Scholar]
  54. LeeH.S. Antiplatelet property of Curcuma longa L. rhizome-derived ar-turmerone.Bioresour. Technol.200697121372137610.1016/j.biortech.2005.07.00616112857
    [Google Scholar]
  55. PrakashP. MisraA. SurinW.R. JainM. BhattaR.S. PalR. RajK. BarthwalM.K. DikshitM. Anti-platelet effects of Curcuma oil in experimental models of myocardial ischemia-reperfusion and thrombosis.Thromb. Res.2011127211111810.1016/j.thromres.2010.11.00721144557
    [Google Scholar]
  56. LiaoJ.C. TsaiJ.C. LiuC.Y. HuangH.C. WuL.Y. PengW.H. Antidepressant-like activity of turmerone in behavioral despair tests in mice.BMC Complement. Altern. Med.201313129910.1186/1472‑6882‑13‑29924176021
    [Google Scholar]
  57. NishiyamaT. MaeT. KishidaH. TsukagawaM. MimakiY. KurodaM. SashidaY. TakahashiK. KawadaT. NakagawaK. KitaharaM. Curcuminoids and sesquiterpenoids in turmeric (Curcuma longa L.) suppress an increase in blood glucose level in type 2 diabetic KK-Ay mice.J. Agric. Food Chem.200553495996310.1021/jf048387315713005
    [Google Scholar]
  58. KurodaM. MimakiY. NishiyamaT. MaeT. KishidaH. TsukagawaM. TakahashiK. KawadaT. NakagawaK. KitaharaM. Hypoglycemic effects of turmeric (Curcuma longa L. rhizomes) on genetically diabetic KK-Ay mice.Biol. Pharm. Bull.200528593793910.1248/bpb.28.93715863912
    [Google Scholar]
  59. KuttanR. LijuV.B. JeenaK. An evaluation of antioxidant, anti-inflammatory, and antinociceptive activities of essential oil from Curcuma longa. L.Indian J. Pharmacol.201143552653110.4103/0253‑7613.8496122021994
    [Google Scholar]
  60. TakemotoY. KishiC. EhiraH. MatsuiN. YamaguchiT. YoshiokaY. MatsumuraS. MoriyamaT. ZaimaN. Inhaled turmerones can be incorporated in the organs via pathways different from oral administration and can affect weight-gain of mice.Sci. Rep.20221211103910.1038/s41598‑022‑15168‑935773461
    [Google Scholar]
  61. JankasemM. Wuthi-udomlertM. GritsanapanW. Antidermatophytic properties of Ar-turmerone, turmeric oil, and Curcuma longa preparations.ISRN Dermatol.201320131310.1155/2013/25059724066236
    [Google Scholar]
  62. Dias FerreiraF. MossiniS.A. Dias FerreiraF.M. ArrotéiaC.C. da CostaC.L. NakamuraC.V. MachinskiM.Jr The inhibitory effects of Curcuma longa L. essential oil and curcumin on Aspergillus flavus link growth and morphology.Sci. World J.2013201334380424367241
    [Google Scholar]
  63. EssienE. NewbyJ. WalkerT. SetzerW. EkundayoO. Chemotaxonomic characterization and in-vitro antimicrobial and cytotoxic activities of the leaf essential oil of Curcuma longa grown in Southern Nigeria.Medicines20152434034910.3390/medicines204034028930216
    [Google Scholar]
  64. DhingraO.D. JhamG.N. BarcelosR.C. MendonçaF.A. GhivirigaI. Isolation and identification of the principal fungitoxic component of turmeric essential oil.J. Essent. Oil Res.200719438739110.1080/10412905.2007.9699312
    [Google Scholar]
  65. AliA.H. AgustarH.K. HassanN.I. LatipJ. EmbiN. SidekH.M. Data on antiplasmodial and stage-specific inhibitory effects of Aromatic (Ar)-Turmerone against Plasmodium falciparum 3D7.Data Brief20203310659210.1016/j.dib.2020.10659233318979
    [Google Scholar]
  66. AmaralA.C.F. GomesL.A. SilvaJ.R.A. FerreiraJ.L.P. RamosA.S. RosaM.S.S. VermelhoA.B. RodriguesI.A. Liposomal formulation of turmerone-rich hexane fractions from Curcuma longa enhances their antileishmanial activity.BioMed Res. Int.201420141810.1155/2014/69493425045693
    [Google Scholar]
  67. TelesA.M. RosaT.D.S. MouchrekA.N. Abreu-SilvaA.L. CalabreseK.S. Almeida-SouzaF. Cinnamomum zeylanicum, Origanum vulgare, and Curcuma longa essential oils: Chemical composition, antimicrobial and antileishmanial activity.Evid. Based Complement. Alternat. Med.2019201911210.1155/2019/242169530766611
    [Google Scholar]
  68. MurakamiA. FurukawaI. MiyamotoS. TanakaT. OhigashiH. Curcumin combined with turmerones, essential oil components of turmeric, abolishes inflammation-associated mouse colon carcinogenesis.Biofactors201339222123210.1002/biof.105423233214
    [Google Scholar]
  69. SunL. ZongS.B. LiJ.C. LvY.Z. LiuL.N. WangZ.Z. ZhouJ. CaoL. KouJ.P. XiaoW. The essential oil from the twigs of Cinnamomum cassia Presl alleviates pain and inflammation in mice.J. Ethnopharmacol.201619490491210.1016/j.jep.2016.10.06427780753
    [Google Scholar]
  70. KimD. SuhY. LeeH. LeeY. Immune activation and antitumor response of Ar-turmerone on P388D1 lymphoblast cell implanted tumors.Int. J. Mol. Med.201331238639210.3892/ijmm.2012.119623229920
    [Google Scholar]
  71. ShanF. YimingM. HeyingZ. ChengS. QiushiW. XianghongY. WeiZ. HuaweiZ. ShanF. Maturation and upregulation of functions of murine dendritic cells (DCs) under the influence of purified aromatic-turmerone (AR).Hum. Vaccin. Immunother.20128101416142410.4161/hv.2152623095866
    [Google Scholar]
  72. OnumaK. SuenagaY. SakakiR. YoshitomeS. SatoY. OgawaraS. SuzukiS. KuramitsuY. YokoyamaH. MurakamiA. HamadaJ. NicolsonG.L. KobayashiM. FujiiJ. OkadaF. Development of a quantitative bioassay to assess preventive compounds against inflammation-based carcinogenesis.Nitric Oxide201125218319410.1016/j.niox.2011.02.00321345376
    [Google Scholar]
  73. HongC.H. NohM.S. LeeW.Y. LeeS.K. Inhibitory effects of natural sesquiterpenoids isolated from the rhizomes of Curcuma zedoaria on prostaglandin E2 and nitric oxide production.Planta Med.200268654554710.1055/s‑2002‑3256012094302
    [Google Scholar]
/content/journals/cmc/10.2174/0929867331666230907112441
Loading
/content/journals/cmc/10.2174/0929867331666230907112441
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error
Please enter a valid_number test