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Block #2,766,665

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 7/26/2018, 10:17:21 PM Β· Difficulty 11.6652 Β· 4,050,167 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dbd996678537cef91916b76f1c937835af3f927658c8938deea42a3bc6430191
View on Chainz β†—

Height

#2,766,665

Difficulty

11.665234

Transactions

2

Size

538 B

Version

2

Bits

0baa4cc5

Nonce

614,296,396

Timestamp

7/26/2018, 10:17:21 PM

Confirmations

4,050,167

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

8aac29b3a76c7056bdec8cf23b4814720ccc3fe18c3de4503ec21debef8e0299
Transactions (2)
Coinbase01f04f1b6f9679…731b8e4d3b50d6
1 in β†’ 1 out7.3500 XPM109 B
AZtxQr2F…7grUWrUz
80e07665ce5b7f…4913798a7974bb
2 in β†’ 2 out12.0900 XPM338 B
AKD9LeNP…bQTn8mEfAcyv2onP…FBfsdmF6
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.

1.777 Γ— 10⁹⁢(97-digit number)
17771633565678416674…04165595968342056959
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
1.777 Γ— 10⁹⁢(97-digit number)
17771633565678416674…04165595968342056959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.777 Γ— 10⁹⁢(97-digit number)
17771633565678416674…04165595968342056961
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
3.554 Γ— 10⁹⁢(97-digit number)
35543267131356833348…08331191936684113919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.554 Γ— 10⁹⁢(97-digit number)
35543267131356833348…08331191936684113921
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
7.108 Γ— 10⁹⁢(97-digit number)
71086534262713666697…16662383873368227839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.108 Γ— 10⁹⁢(97-digit number)
71086534262713666697…16662383873368227841
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
1.421 Γ— 10⁹⁷(98-digit number)
14217306852542733339…33324767746736455679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.421 Γ— 10⁹⁷(98-digit number)
14217306852542733339…33324767746736455681
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
2.843 Γ— 10⁹⁷(98-digit number)
28434613705085466679…66649535493472911359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.843 Γ— 10⁹⁷(98-digit number)
28434613705085466679…66649535493472911361
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
5.686 Γ— 10⁹⁷(98-digit number)
56869227410170933358…33299070986945822719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
5.686 Γ— 10⁹⁷(98-digit number)
56869227410170933358…33299070986945822721
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:57,778,696 XPMΒ·at block #6,816,831 Β· updates every 60s
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