XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,789,043

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/11/2018, 9:35:15 AM Β· Difficulty 11.6725 Β· 4,053,123 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
619478a341f18c7bf0b183cf84a2700b6cb2abe0e8305121d2808c615915e07a
View on Chainz β†—

Height

#2,789,043

Difficulty

11.672467

Transactions

1

Size

201 B

Version

2

Bits

0bac26c7

Nonce

434,497,204

Timestamp

8/11/2018, 9:35:15 AM

Confirmations

4,053,123

Mined by

⛏️ P2SHAUe3MkC7ygDtTzsem25QnsubDp8gimckwF

Merkle Root

0d5baaf968007c5522b4fd4d54805331a0d05085bfb5fc9f9032b9ffdcba4b9b
Transactions (1)
Coinbase0d5baaf968007c…32b9ffdcba4b9b
1 in β†’ 1 out7.3300 XPM110 B
AUe3MkC7…8gimckwF
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.

1.003 Γ— 10⁹⁷(98-digit number)
10037926663785393547…10335104399588823039
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
1.003 Γ— 10⁹⁷(98-digit number)
10037926663785393547…10335104399588823039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.003 Γ— 10⁹⁷(98-digit number)
10037926663785393547…10335104399588823041
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
2.007 Γ— 10⁹⁷(98-digit number)
20075853327570787094…20670208799177646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.007 Γ— 10⁹⁷(98-digit number)
20075853327570787094…20670208799177646081
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
4.015 Γ— 10⁹⁷(98-digit number)
40151706655141574189…41340417598355292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.015 Γ— 10⁹⁷(98-digit number)
40151706655141574189…41340417598355292161
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
8.030 Γ— 10⁹⁷(98-digit number)
80303413310283148379…82680835196710584319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.030 Γ— 10⁹⁷(98-digit number)
80303413310283148379…82680835196710584321
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
1.606 Γ— 10⁹⁸(99-digit number)
16060682662056629675…65361670393421168639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.606 Γ— 10⁹⁸(99-digit number)
16060682662056629675…65361670393421168641
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
3.212 Γ— 10⁹⁸(99-digit number)
32121365324113259351…30723340786842337279
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.212 Γ— 10⁹⁸(99-digit number)
32121365324113259351…30723340786842337281
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:57,981,719 XPMΒ·at block #6,842,165 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