Last weekend turned out to be Food Weekend. Haha, Not sure what to make of it but stuff just happened, so here's a food or two consumed by yours truly just because.
First off, Siomai.
I don't really eat siomai. I don't really have a reason to. My friends can attest to the fact that I really avoid eating it if I can help it. Saturday proved to be an exception to the rule. A friend brought siomai for taste-test and I enjoyed eating it, even the chili sauce.
There were two types of Siomai for the taking,
First is the Japanese Siomai which my friends always eat. It tasted great, much better when we squeezed calamansi over it and dip it in the accompanying chili sauce. I always thought that siomai tasted like the wonton people put in pancit molo, but nah they don't quite taste the same. The siomai tasted finer, haha.
The second one is Shark's Fin Siomai. This one tasted like the steamed shark's fin you eat in Chinese Restos or the fried ones you eat from the Fishball Stalls at the mall. It was chewy and tasted like meat. I wouldn't mind eating this one again.
So I liked the second one better. Not that the first one was bad, it was just something you see everyday everywhere.
Anyhow, my friend is selling Siomai and Siopao and 45-day free range chicken. So if you are in the vicinity of Iloilo City, you can order some. Let me know in the comments and I'll put in a word for you.
Daghang salamat sa pagbasa!!!
Random places. Random events. My thoughts on them and the inspiration they provide for me to be able to write the things you will be reading on this graffiti wall called Blogger.
About Me
- Jeng Martinez
- Iloilo City, Region VI ILOILO, Philippines
- No longer as young but still struggling to write things
Friday, March 31, 2017
Tuesday, March 28, 2017
Semester Break Escapade Part 3: Mambukal Resort
Another hour of road trip, this time to Murcia, Negros Occidental for our overnight stay at Mambukal Resort. We had to pay a 50 pesos entrance for each person before entering the resort.
Mambukal Entrance Sign |
Our accommodation is a villa with 4 beds, a bathroom, and a CR. Shortly after arriving, we unpacked and had our dinner. The food was so good and cheap, and the service instantaneous. Starving as I was before the meal, I was so full afterwards that sleep is a good option.
Sulfur Hot Spring |
At 10:00 PM, the pool closes. We showered and dressed, played some cards and drink some tequila before turning in for the night.
Early on the next day, at 7:30 AM after a breakfast of sandwiches, we trekked on to the 7th falls advertised as one of the to-do things when in Mambukal. Before the climb, we passed by the area where the bats roost at the day, and some are really large. This is also one of the activities offered by the resort: Bat Watching.
Lone Bat at Dawn |
It was a very steep climb with rocks and trees, the only things surrounding you for hours. Oh, and the occasional bats, when they were disturbed by other trekkers. But the breathtaking falls on every stop make it worth the climb.
trek to the 7th falls |
2nd Falls |
Rest stop on the 5th and 6th falls |
7th Falls Swim |
At the 7th, we rested for a while and had a falls massage. This is my 2nd time on Mambukal but the falls is really preserved and protected. The water very clear and cool. We also refilled our water containers for the climb down. On the way down, we use a different route which was not as steep as the way of the falls. The trek was only for 2 ½ hours and we paid the guide 500 pesos.
Upon arriving at the resort, we directly took a dip at the hot spring again. This, by the way, comes free with the accommodation we have. The hot spring or the swimming pool are the choices.
After 30 minutes or so on the pool, we decided to shower and change and also check out of the villa. We had our lunch at the restaurant and it was a banquet. Well, with all those things we ordered, it certainly looked and felt like one. We had pork, scallops, pancit guisado, fish and a lot of rice plus drinks. And there were only 11 of us eating and we consumed everything in sight. After the meal, we did a little sightseeing like buying flowers and plants.
Boating Pond |
Mambukal also offers boating, slide for life and wall climbing. We were not able to do this things, but we just visited the butterfly garden for the souvenirs and other stuffs.
Then we have the ride back to Bacolod City. We passed by a Tanduay Distillery, San Miguel Brewery and the Coca-Cola Plant which we did not see on the way to.
At Bacolod City, we stopped by Merci to buy some pasalubong. Then off to Bacolod Port for the journey home on the 5:15 PM trip on the Ocean Jet Ferry again. At 7:00 PM we are back on Iloilo City with a welcome of a pouring rain.
That’s end of the journey for my Semester Break escapade. Now off to write about our previous trips.
Part 1
Part 2
Part 1
Part 2
Daghang salamat sa pagbasa!!!
Saturday, March 25, 2017
Bacon Pancake
The other day, the hubby and I were deciding on what to eat for dinner. I wanted pancakes. He wanted bacon. So in jest, I said let's have Bacon Pancakes for dinner.
When I googled Bacon Pancakes, wonders of wonders there is a Bacon Pancake result, not including the Bacon Pancake song from Adventure Time.
Here's our slightly altered recipe of BACON PANCAKES.
Ingredients:
Preparation:
Daghang salamat sa pagbasa!!!
When I googled Bacon Pancakes, wonders of wonders there is a Bacon Pancake result, not including the Bacon Pancake song from Adventure Time.
Here's our slightly altered recipe of BACON PANCAKES.
Ingredients:
- Bacon Slice
- Pancake Mixture
- Salt
- Ground Pepper
Preparation:
- Place 10-12 pieces of Bacon Slice in a bowl, sprinkle with some salt and pepper. 1/8 tsp or less of each should do the trick.
- In a separate bowl, prepare the Pancake Mixture. I actually use a ready-made one, so I just add an egg and some water. Do not add the usual amount of water you usually use so that the mixture will be slightly thicker than the normal pancake.
- Heat a flat pan over the fire, and place the bacon slice in it. Cook each side of the bacon for 3-5 minutes. Set aside the cooked bacon.
- Remove bacon oil from the pan.
- Place 1-2 cooked bacon in the pan, pour 2 tbsp (or more) of pancake mixture over it. Once it bubbles, flip the bacon pancake to cook the other side.
- Cook all slices in this manner.
- Eat after cooking. Enjoy!
So there you have it, folks!!!
Enjoy your breakfast, I mean meal :D
Daghang salamat sa pagbasa!!!
Labels:
bacon,
bacon pancake,
bacon slice,
food,
home cooking,
pancake,
pancake mixture
Wednesday, March 22, 2017
Semester Break Escapade Part 2: Campuestohan Highland Resort
After an hour of taking pictures at The Ruins, we again went on a one-hour road trip to Campuestohan Highland Resort.
The accommodation for the day trip includes some huts around the swimming pool area, some lounge on the villas and a canopy tent on the grounds. It costs 300 to 1000 pesos depending on size and location. For overnight stay, they have the Bonita Huts which is good for 4 for 2500 pesos. The Log Cabins for 3000, 4000 and 5000 pesos good for 3, 4 and 5 persons respectively. Extra persons costs 500 pesos exclusive of breakfast. The night accommodation is inclusive of breakfast and entrance fees.
The Sky Bicycle looks fun and my friends enjoyed their ride. I think it’s a very exhilarating experience judging by their expressions. But if you have fears like the author, hehe, I don’t really go for heights. It’s located at about 700 meters to 1000 meters from the ground. And the only means of support is the bike and the rope around your waist. I did enjoy strolling on the hanging bridge, so that makes up for it.
After the Sky Bicycle, we had our lunch at the resorts restaurant on Buttered Chicken, Chicken Binakol, Pork Sinigang, some seafood meal, different drinks and rice. The food tastes great, though the service is not as fast as we wanted it to be. Well, it was also after lunch time so there is a fewer staff working, I think. Definitely needs improvement on service but food is tasty, so let bygones be bygones.
After the meals, we had our picture taking on the different figures around the resort. All around the 15-hectare land area, if I remember correctly, are different statues of our favorite characters. They have the Avengers, Son Goku, Michael Jordan, Spoon and Fork and Veggies at the entrance of the restaurant, the Dragon Warrior and the Furious Five, Bumble Bee, Optimus Prime and a giant King Kong that bellows from time to time.
I really wanted to try the Rope Course, it looks so inviting, but we didn’t have any time and there are still some people who are trying it out. So we didn’t pursue that one and just strolled on the ground.
The place is so relaxing and so fresh. Just sitting there, eating ice cream and chips is a feel good experience. I hope to get back there one day and take my revenge on that Rope Course.
Daghang salamat sa pagbasa!!!
It is located in Sitio Cabatangan, Brgy. Campuestohan, Talisay City on the side of the mountain. So going there, without a private means of transportation is not only a hassle but also a bit costly. So, if going solo, there is a shuttle provided for by Campuestohan that leaves at 9:00 AM from Villa Angela Arcade parking lot (front of Lopue’s East Corner), Bacolod City and 4:00 PM from the resort. The fare is 100 pesos to and from the resort.
The entrance fee for Campuestohan is 150 pesos for each person, this is inclusive of the swimming pool and the park rides. They also have the following activities offered: The Sky Bicycle for 100 pesos, Zip Line for 200 pesos, Horseback Riding for 150 pesos, and Rope Course for 200 pesos.
Bonita Huts Accomodation |
Sky Bicycle for 100 php |
View from Hanging Bridge |
Buttered Chicken for Lunch |
Restaurant Sign |
King Kong |
Dragon Warrior and the Furious Five |
Rope Course for 200 php |
The place is so relaxing and so fresh. Just sitting there, eating ice cream and chips is a feel good experience. I hope to get back there one day and take my revenge on that Rope Course.
At 4:00 PM, we left Campuestohan behind and journeyed to our next stop: Mambukal Resort. But before proceeding there, we stop by Bacolod City to buy some bread and other essentials.
And onto the next post.
Part 1Daghang salamat sa pagbasa!!!
Monday, March 20, 2017
Movie Review: Beauty and the Beast
Warning! Spoilers Ahead!
Daghang salamat sa pagbasa!!!
Photos from:
http://www.comingsoon.net/movies/news/827575-beauty-and-the-beast-roars#/slide/1
http://www.insidethemagic.net/2016/08/photos-first-look-at-lumiere-cogsworth-and-gastons-tavern-in-disneys-live-action-beauty-and-the-beast-movie/
Missing the entire opening scene, because as always I am so
late into getting inside the cinema. A friend did say that it was just a
narrative the same as the animated series. Since I watched that before watching
this, I guess I am confident enough to say I did not miss anything that great.
It was a very nice movie, that by the end of it, I was
clapping loudly and wanted to pair it with a standing ovation, but I held back to
respect the people sitting behind me.
The plot is the same as the animated one with some minor
changes here and there.
Let’s start with what I did not like since I can count them
in one hand.
First, some scenes were
so obviously in 3D it’s just a blur. It has a start and end points that you can
see, then just become glassy in the middle and I was wearing glasses so it is
not an eye problem. Second, I am not
sure if I missed it but there was no Human
Again song in the movie, and I quite liked that song. Third, there were some scenes that were very dark and cannot be
really scene clearly, and I think some of those dark scenes on-screen were not
in 3D and not the Beast’s brooding aura as well. Fourth, some of Emma Watson’s facial expressions does not quite fit
the emotion she is portraying but I can forgive that. I think I just have
problems with her and it has nothing to do with the movie. :D (I am so screwed, sorry friends. I’m a fan
too :D)
Now for the goods. I think I’ll do a character evaluation
and make it flow with the story.
The music for this movie is so great and since
its Alan Menken, we know we can
always expect the best.
The story started with Belle who is not a snob, not in a
long shot but she has an air about her that screamed ‘I am too good, for this
town. When can I leave it all behind?’. She lived with her father, Maurice, who
is not as kooky as he was in the animated series but is still an oddity, an
outsider artisan. She is being courted by the best character portrayal in town,
Luke Evans as Gaston, who is clearly
a beautiful person and deserves to be married to the second eye-candy in town
right after himself. Captain Gaston is home from the war and is suffering from PTSD, Post-Traumatic Stress Disorder,
which explains his bursts in rage among other things. And did I mention, he is narcissistic
to the bone. Hanging to Gaston’s sleeves is LeFou whose heroic worship was turned into unrequited love. He will
do anything for Gaston, and that includes paying off everybody so that they
will participate in the Gaston song. That song was one of the best scenes ever
and it was a replicate of the animated one and showed us exactly how great actors
Josh Gad and Luke Evans that they
can transform a well-loved scene from a cartoon to a movie without the added
help of animation.
And now to the wolves, I meant castle.
Lumiere is played
by Obi-wan Kenobi. This is one of those character portrayal that is more
popularly than the lead and is shrouded in controversy because Ewan McGregor is not one though he
married one. But it was great character and I loved every moment that he was
on-screen. Cogsworth is played by Sir Ian McKellen and I actually forgot
that it was him and was thinking the entire time he appears that this voice is
very very familiar and I could not quite place where I heard it before. It was Gandalf all along, no wonder he did
not have any singing scenes, only singsong ones. Mrs. Potts and Chip, were portrayed as they were including that
heartfelt rendition of Tale as As Old
Time, I meant, Beauty and the Beast.
Though they did not made Chip a stowaway and made him attack the cellar to
free Belle and her father, it was overall a nice performance. The rest of the castle
folks were as they were, since they rarely appeared on screen, I cannot really
say a lot about them. And as I have forgotten, and was typing the line before I remembered,
I did not wrote anything about the Beast.
The Beast was portrayed not as dark as he was in the animated one actually. This
is one beast that you can actually fall in love in, not that you know
beforehand that a handsome animal is actually playing this character but
because of the nature he was presented. From a terrorizing person who is quick
to defend his own, a giving host that shares his books and jokes, a person who
understands you and made something clear a part of your childhood that your
father is shielding you from, and someone who let you go when he knows that
keeping you will only make you hate him forever. But I think it was the
Shakespeare’s quote that did me in. Haha!
My favorite part of the movie is the Be Our Guest song. When it was finished I was clapping in glee. It was
the highlight of the movie for me. Not the transformation of the Beast to the
Prince. Not the resurrection of forgotten persons to human beings again. But that
song, the song where they refused to let Belle eat the steak and only served
her a pudding afterwards.
It was also good that they gave us a background story on
Belle and the Beast. Like why Belle does not really fit in, because she was not
born in the village but was brought here by her father when her mother died. And
the Beast is not really mean-spirited, he was a young sweet boy whose cruel
father turned into a monster when his lovely mother died. This is why we can
now understand the changes in his feelings and attitudes, because he has always
have them but was just shadowed with the cruelty that he has to live with.
The emotions in this movie are also great, like the
desperation of Gaston to make Belle his and that he would do anything for it,
including locking up her father. LeFou’s blind devotion to the man he adores
that turned into betrayal because he was betrayed first. The anger of the villager
towards Belle when she tried to teach another girl to read. The jealousy
because she was a pretty lass. The confusion the villagers felt when they
entered the castle and it felt familiar. The acceptance the castle furniture
felt when they know they will be forever forgotten and started turning to
antiques. The joy when everything turned back to being humans, and family and lovers
reunited again, except for Cogsworth who actually prefers being to a clock than
being with his wife. The peace that followed.
I liked this movie, not only because it’s a childhood
classic but because it tried to balance itself in this changing times, i.e, the
depiction of gender and race equality. So we have men falling in love with men,
men coming out of the closet, women fighting for themselves, thinking for
themselves. Gender equality and women empowerment. The world’s most controversial files. I think accepting this role is
one way for Emma Watson to promote her HeForShe campaign as well as remind us
of her role as UN Women Goodwill Ambassadress. Also, there were lots of colored
French characters in this film, and yes it’s quite alright. Not only that it’s
historically true, it was a nice distribution of roles too. So many talented
people in one place, singing their hearts out.
I hope that was not as spoiled as it should be. But if you’ve
watched the animated classic, there’s really nothing left to spoil.
Photos from:
http://www.comingsoon.net/movies/news/827575-beauty-and-the-beast-roars#/slide/1
Saturday, March 18, 2017
Semester Break Escapade Part 1: The Ruins
Ruins - Front View |
On October 25, 2014, after months of planning to get away from the city of Iloilo, we finally did it. We scheduled a 2-day trip to the neighboring province Negros Occidental. A trip on some of its famous landmarks. We have The Ruins, Campuestohan Highland Resort and Mambukal Resort on our list.
I had broken this trip into a 3-part series.
First, let’s discuss our reservations. Our sleeping place will be at the Mambukal Resort, we had a room reserved for we thought a month. It turned out, we had been had and no reservations was reserved because the guy we first talk to did not forward our request to the reservations office. Fortunately, the girls at the Office of the Governor pulled through. So, to avoid disasters in your future trips, please call +63 (34) 433-8516. This is the official number for reservations. In the end, instead of paying 3000 pesos for 2 rooms, we paid 4800 pesos for 2 rooms with 200 pesos additional for each person extra. We deposited 3000 pesos in advance for the accommodation to the Negros Occidental provincial account.
Second is our means of transportation. Some of the places we are eyeing to go to are far from the Bacolod City and transportation means may not be easily attained. Good for us, an officemate recommended a shuttle van service. We paid 6000 pesos for the whole trip. If you want his number for your future trips, please email us.
Now that 2 major problems are taken care of, what is left to do is get there.
Port of Iloilo |
So early in the morning, 5:00 AM, we ride on a taxi to get to the new Iloilo Port at La Puz, Iloilo City.
There are also jeepneys who pass through the new port. Just ask the driver if he will pass on the new port. The fare will be 7.50 pesos. We rode on the 6:15 AM Ocean Jet ferry bound for Bacolod City. The ferry costs 245 pesos for one person.
While on the ferry, I texted Mr. Raymond, that’s the name of our driver for the trip, that we were on our way.
Bob’s Cafe, 21st Lacson St. Iloilo City |
At 7:45 AM, we arrive at the Port of Bacolod. We met up with Mr. Raymond and proceed with first agenda of the day: BREAKFAST.
After driving around, we had our breakfast at Café Bobs at 21st St., Bacolod City. It was an enjoyable meal, the place is cozy and the food is good.
After the meal, we traveled for 30 minutes or so to Talisay City and arrive at The Ruins. It’s actually easy to locate now because every sign post leading to it has sign that reads: This way to The Ruins.
The first indication of the place was a tall ancient tower that looks like a lighthouse beckoning us to come nearer. And at that place, directly in front of it is the gates to The Ruins. It had an entrance fee of 100 pesos per person and a 40 pesos fee for students.
Old Mill Tree |
The first indication of the place was a tall ancient tower that looks like a lighthouse beckoning us to come nearer. And at that place, directly in front of it is the gates to The Ruins. It had an entrance fee of 100 pesos per person and a 40 pesos fee for students.
Maria Braga – top right |
After a fire that destroyed the mansion during World War 2, what remained is a beautiful structure that will stir your heart in its beauty and you can envision how it must have looked like in its heyday. Most people say, that The Ruins is doubly beautiful at night. But during the day, one can still see that it’s a great piece of architecture.
The inside of The Ruins looks sturdy and some of the parts have been repaired or reconstructed to their look during the old days.
Arcs |
Walls |
Stairs to second floor |
Around the ruins now, a fountain has been built and the garden has been landscaped. Some architectural tributes were also constructed.
Architects of the Philippines |
Fountain |
Fountain with Ruins Side |
In front of the mansion, a restaurant is also added where you can eat and cool down. Though we did not stay to eat, so I could not really comment on the food.
And if you go there at around noon, don’t forget to bring an umbrella.
Ruins – Side View |
Daghang salamat sa pagbasa!!!
Wednesday, March 15, 2017
Ovenless Pizza
Because the hubby wanted to eat pizza and being in the rain is not really an ideal place to be with a takeout box, we decided to make one at home. The challenge, we do not have an oven. Not yet, anyway.
So this is NOT a baked pizza, it's a steamed one.
First, the ingredients:
Actually, we made two a square and a circle, we just forgot to take a picture of the second one because we were too excited to eat.
For the circle pizza, we actually added cheese to the side of the crust before we grilled it.
Also, this activity took us two hours before we were able to eat. So it's not advisable to do if you are hungry and need to eat ASAP.
But on lazy weekends, you can do this, as you have all the time in the world.
So enjoy your pizza,!!
Bon appetit!
Daghang salamat sa pagbasa!!!
So this is NOT a baked pizza, it's a steamed one.
First, the ingredients:
cheese, bell pepper, onions |
meat, pepperoni, sausage, dough |
- For the dough, you can either buy the ready-made one from the grocery or make your own like we did.
Mix flour with water in a bowl until it's a sticky mixture. Then knead the dough for 10minutes and let it be. - For the toppings, we usually go over the top on what we put in our pizza since it is ours and we can do whatever we want with it.
MEAT: Bacon, Pepperoni, Hungarian Sausage sliced as thinly as the pepperoni, and leftovers from the Giniling Guisado (Ground Beef) viand we had the day before
CHEESE: Grated Parmesan, Grated Cheddar Cheese, and thinly sliced Mozzarella
PIZZA SAUCE: Tomato Sauce mixed with Ground Black Pepper
ONIONS and BELL PEPPER.
HOW WE MADE THE PIZZA
- Place all the meat products in a pan and cook until dry, since these are all cooked anyway and just needed a bit of heating. Cook and then set aside.
- Shape the dough into a circle or square pizza crust. Using a flat pan, grill the pizza dough until it's also dry and looking like a pita bread. Grill both sides.
- Once, the pizza crust is grilled enough, add the toppings.
- Spread the pizza crust with pizza sauce, sprinkle with Parmesan, add the meat toppings, then onions and bell pepper, then add the cheese toppings.
- Heat a flat pan over medium to high heat. Add some water to check if the pan is hot enough and will produce steam. If it does, place the pizza crust with toppings in the pan.Then, add some more water, be careful not to pour any on the pizza, then cover it up.
- Check from time to time if the water has gone dry or if the Mozzarella has melted.
- Add water to steam until the Mozzarella has melted, this is your indication that the pizza is ready.
With that, we had a tasty home-made pizza.
Actually, we made two a square and a circle, we just forgot to take a picture of the second one because we were too excited to eat.
For the circle pizza, we actually added cheese to the side of the crust before we grilled it.
Also, this activity took us two hours before we were able to eat. So it's not advisable to do if you are hungry and need to eat ASAP.
But on lazy weekends, you can do this, as you have all the time in the world.
So enjoy your pizza,!!
Bon appetit!
Daghang salamat sa pagbasa!!!
Sunday, March 12, 2017
Fermat Factorization Method
Pierre de Fermat |
In his method, Fermat assumes that n is odd and observed that the search for factors of n is equivalent to obtaining the integral solutions of x and y of the equation n = (x^2) – (y^2) = (x – y) (x + y)
If n has a factorization n = ab, a ≥ b ≥ 1
We may write n = ((a+b)/2)^2 – ((a-b)/2)^2 ; (a+b)/2 > 0 and (a-b)/2 > 0
We may write n = ((a+b)/2)^2 – ((a-b)/2)^2 ; (a+b)/2 > 0 and (a-b)/2 > 0
We then determine the smallest integer k for which k^2 ≥ n, k^2 – n, (k+1)^2 – n, (k+2)^2 – n, … until a value of m ≥ √n is found making m^2 – n a square.
We know that this process cannot go on indefinitely, we know we will eventually arrive at ((n+1)/2)^2 – n = ((n-1)/2)^2, the representation of n corresponding to the trivial factorization n = n ∙ 1. Meaning that n is a prime.
Examples:
1. n = 2027651281, k= 45030
45030^2 – 2027651281 = 49619
45031^2 – 2027651281 = 139680
45032^2 – 2027651281 = 229743
45033^2 – 2027651281 = 319808
45034^2 – 2027651281 = 409875
45035^2 – 2027651281 = 499944
45036^2 – 2027651281 = 590015
45037^2 – 2027651281 = 680088
45038^2 – 2027651281 = 770163
45039^2 – 2027651281 = 860240
45040^2 – 2027651281 = 950319
45041^2 – 2027651281 = 1040400 = 1020^2
=> 2027651281 = 45041^2 – 1020^2
=> 2027651281 = (45041+1020)(45041–1020)
=> 2027651281 = (46061)(44021)
1. n = 2027651281, k= 45030
45030^2 – 2027651281 = 49619
45031^2 – 2027651281 = 139680
45032^2 – 2027651281 = 229743
45033^2 – 2027651281 = 319808
45034^2 – 2027651281 = 409875
45035^2 – 2027651281 = 499944
45036^2 – 2027651281 = 590015
45037^2 – 2027651281 = 680088
45038^2 – 2027651281 = 770163
45039^2 – 2027651281 = 860240
45040^2 – 2027651281 = 950319
45041^2 – 2027651281 = 1040400 = 1020^2
=> 2027651281 = 45041^2 – 1020^2
=> 2027651281 = (45041+1020)(45041–1020)
=> 2027651281 = (46061)(44021)
2. n = 17, k = 5
5^2 – 17 = 8
6^2 – 17 = 19
7^2 – 17 = 32
8^2 – 17 = 47
9^2 – 17 = 64 = 8^2
=> 17 = 9^2 – 8^2
=> 17 = (9 + 8)(9 – 8)
=> 17 = (17)(1)
NOTE:
Squares must end in 0, 1, 4, 5, 6, and 9
And from 0-99 (mod 100) ends in 00, 01, 04, 09, 16, 21, 24, 25, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, 84, 89, 96
Daghang salamat sa pagbasa!!!
Thursday, March 9, 2017
Fermat Numbers
The Fermat Numbers form a sequence in the form
Fn = (2^(2^n)) + 1, n = 0, 1, 2, …
or Fn = pow(2,(pow(2,n))) + 1
or Fn = pow(2,(pow(2,n))) + 1
The number of digits for a Fermat number is
D(Fn) = └[log (2^(2^n))+ 1)] + 1┘
D(Fn) = └[log (2^(2^n))] + 1┘
D(Fn) = 1 + └2^n log 2┘
or D(Fn) = 1 + floor((2^n) log 2)
D(Fn) = └[log (2^(2^n))+ 1)] + 1┘
D(Fn) = └[log (2^(2^n))] + 1┘
D(Fn) = 1 + └2^n log 2┘
or D(Fn) = 1 + floor((2^n) log 2)
The first few Fermat numbers are:
F0 = 2^(2^0) + 1 = (2^1) + 1 = 2 + 1 = 3
F1 = 2^(2^1) + 1 = (2^2) + 1 = 4 + 1 = 5,
F2 = 2^(2^2) + 1 = (2^4) + 1 = 16 + 1 = 17,
F3 = 2^(2^3) + 1 = (2^8) + 1 = 256 + 1 = 257,
F4 = 2^(2^4) + 1 = (2^16) + 1 = 65536 + 1 = 65537
F1 = 2^(2^1) + 1 = (2^2) + 1 = 4 + 1 = 5,
F2 = 2^(2^2) + 1 = (2^4) + 1 = 16 + 1 = 17,
F3 = 2^(2^3) + 1 = (2^8) + 1 = 256 + 1 = 257,
F4 = 2^(2^4) + 1 = (2^16) + 1 = 65536 + 1 = 65537
The corresponding number of digits:
D(F0) = 1 +└(2^0) log 2┘= 1 +└1 log 2┘= 1 + 0 = 1
D(F1) = 1 +└(2^1) log 2┘= 1 +└2 log 2┘= 1 + 0 = 1
D(F2) = 1 +└(2^2) log 2┘= 1 +└4 log 2┘= 1 + 1 = 2
D(F3) = 1 +└(2^3) log 2┘= 1 +└8 log 2┘= 1 + 2 = 3
D(F4) = 1 +└(2^4) log 2┘= 1+└16 log 2┘= 1+ 4 = 5
D(F1) = 1 +└(2^1) log 2┘= 1 +└2 log 2┘= 1 + 0 = 1
D(F2) = 1 +└(2^2) log 2┘= 1 +└4 log 2┘= 1 + 1 = 2
D(F3) = 1 +└(2^3) log 2┘= 1 +└8 log 2┘= 1 + 2 = 3
D(F4) = 1 +└(2^4) log 2┘= 1+└16 log 2┘= 1+ 4 = 5
These numbers are more popularly known as Fermat primes.
F5, F6, F7, F8, F9, F10 and F11 are factorable numbers. F11 being the largest known Fermat number to be factored out.
F5, F6, F7, F8, F9, F10 and F11 are factorable numbers. F11 being the largest known Fermat number to be factored out.
I have created a PHP code for computing the number of digits found in a Fermat number, and the Fermat Number itself if possible.
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