Block #2,292,184

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/11/2017, 2:45:42 PM · Difficulty 10.9550 · 4,551,854 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c242cfa92c8e9ebd812212a0f6b00fac71b6cd8437d29cfdd83a482db8f5186

View on Chainz ↗

Height

#2,292,184

Difficulty

10.954959

Transactions

Size

1.22 KB

Version

Bits

0af47838

Nonce

1,025,755,961

Timestamp

9/11/2017, 2:45:42 PM

Confirmations

4,551,854

Mined by

⛏️ P2SHAYoJ8f2XGuTvtY7WjgPyhBYq9Yx4Ztr3Zt

Merkle Root

0280400537957f86ba6c4d066c02463f778255d4cc7a9c5ab375cb67717a411c

Transactions (5)

Coinbase9b5baa29d9ba43…60f9655fe93f36

1 in → 1 out8.3600 XPM109 B

AYoJ8f2X…x4Ztr3Zt

e5b48ed42a9a00…22b3635077403e

1 in → 2 out6038.9700 XPM226 B

ALxYZvpD…Rz4Quq8U AZzDaqQe…phejW5aP

be56d7c76c846b…e5ee4fad4541cc

2 in → 2 out2337.5594 XPM376 B

Ae4f4RgG…D1VnH2TX AU7xkW52…RMPvkSaU

4fdd8d276d7a59…9040d082ebd176

1 in → 2 out383.0938 XPM226 B

AXTcX6mk…zjcdXfCW AcH7iJpz…kvchpYAj

23533d27e3e947…d8f4fc764f56a7

1 in → 2 out132.2722 XPM226 B

AR5t7E7Q…hK7FDNDe AHrcvaQn…NkKFHQsT

Prime Chain Origin

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

1.848 × 10⁹⁴(95-digit number)

18486088409239414359…96889333688148645929

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.848 × 10⁹⁴(95-digit number)

18486088409239414359…96889333688148645929

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.848 × 10⁹⁴(95-digit number)

18486088409239414359…96889333688148645931

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.697 × 10⁹⁴(95-digit number)

36972176818478828719…93778667376297291859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.697 × 10⁹⁴(95-digit number)

36972176818478828719…93778667376297291861

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

7.394 × 10⁹⁴(95-digit number)

73944353636957657439…87557334752594583719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.394 × 10⁹⁴(95-digit number)

73944353636957657439…87557334752594583721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.478 × 10⁹⁵(96-digit number)

14788870727391531487…75114669505189167439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.478 × 10⁹⁵(96-digit number)

14788870727391531487…75114669505189167441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.957 × 10⁹⁵(96-digit number)

29577741454783062975…50229339010378334879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.957 × 10⁹⁵(96-digit number)

29577741454783062975…50229339010378334881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.915 × 10⁹⁵(96-digit number)

59155482909566125951…00458678020756669759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,292,184

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