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Block #2,187,865

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/1/2017, 11:22:41 AM Β· Difficulty 10.9477 Β· 4,651,674 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8ee4e326147d2609cfaad1b69d451b9b688d9299271b837043339ab5c44c698c
View on Chainz β†—

Height

#2,187,865

Difficulty

10.947663

Transactions

1

Size

201 B

Version

2

Bits

0af29a07

Nonce

151,092,551

Timestamp

7/1/2017, 11:22:41 AM

Confirmations

4,651,674

Mined by

⛏️ P2SHAKjtn8v8fU3iPrEtDdBPCZ8vcNgcckN6pP

Merkle Root

4ec4dbbbda88abced9842cbea4d8f0fb8b7fe8712281b692fa9b58d5606852c8
Transactions (1)
Coinbase4ec4dbbbda88ab…9b58d5606852c8
1 in β†’ 1 out8.3300 XPM110 B
AKjtn8v8…gcckN6pP
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.

1.105 Γ— 10⁹⁢(97-digit number)
11056309174876133430…53382606622432650239
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
1.105 Γ— 10⁹⁢(97-digit number)
11056309174876133430…53382606622432650239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.105 Γ— 10⁹⁢(97-digit number)
11056309174876133430…53382606622432650241
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
2.211 Γ— 10⁹⁢(97-digit number)
22112618349752266861…06765213244865300479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.211 Γ— 10⁹⁢(97-digit number)
22112618349752266861…06765213244865300481
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
4.422 Γ— 10⁹⁢(97-digit number)
44225236699504533722…13530426489730600959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.422 Γ— 10⁹⁢(97-digit number)
44225236699504533722…13530426489730600961
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
8.845 Γ— 10⁹⁢(97-digit number)
88450473399009067445…27060852979461201919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.845 Γ— 10⁹⁢(97-digit number)
88450473399009067445…27060852979461201921
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
1.769 Γ— 10⁹⁷(98-digit number)
17690094679801813489…54121705958922403839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.769 Γ— 10⁹⁷(98-digit number)
17690094679801813489…54121705958922403841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,960,603 XPMΒ·at block #6,839,538 Β· updates every 60s
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