XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,661,924

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/15/2018, 10:31:21 AM Β· Difficulty 11.6369 Β· 4,181,382 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
bbd0e4dde8bfa48be91971d243340d20e381970a5bea0537d5dbd6367217614a
View on Chainz β†—

Height

#2,661,924

Difficulty

11.636931

Transactions

1

Size

200 B

Version

2

Bits

0ba30de5

Nonce

854,992,470

Timestamp

5/15/2018, 10:31:21 AM

Confirmations

4,181,382

Mined by

⛏️ P2SHARK5dkYcaKhzL6W9zghoWbgjiKwR1Dg7wj

Merkle Root

6d548da0b6310111a861c56b8ee6c12db8d8e51b395fde136333f4da8f10dc94
Transactions (1)
Coinbase6d548da0b63101…33f4da8f10dc94
1 in β†’ 1 out7.3700 XPM110 B
ARK5dkYc…wR1Dg7wj
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.420 Γ— 10⁹⁡(96-digit number)
34203199795442075567…65106625071020026879
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.420 Γ— 10⁹⁡(96-digit number)
34203199795442075567…65106625071020026879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.420 Γ— 10⁹⁡(96-digit number)
34203199795442075567…65106625071020026881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
6.840 Γ— 10⁹⁡(96-digit number)
68406399590884151134…30213250142040053759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.840 Γ— 10⁹⁡(96-digit number)
68406399590884151134…30213250142040053761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.368 Γ— 10⁹⁢(97-digit number)
13681279918176830226…60426500284080107519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.368 Γ— 10⁹⁢(97-digit number)
13681279918176830226…60426500284080107521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.736 Γ— 10⁹⁢(97-digit number)
27362559836353660453…20853000568160215039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.736 Γ— 10⁹⁢(97-digit number)
27362559836353660453…20853000568160215041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.472 Γ— 10⁹⁢(97-digit number)
54725119672707320907…41706001136320430079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.472 Γ— 10⁹⁢(97-digit number)
54725119672707320907…41706001136320430081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.094 Γ— 10⁹⁷(98-digit number)
10945023934541464181…83412002272640860159
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.094 Γ— 10⁹⁷(98-digit number)
10945023934541464181…83412002272640860161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,990,814 XPMΒ·at block #6,843,305 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy