Block #243,227

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 4:25:59 AM · Difficulty 9.9612 · 6,601,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3022732de459644af64f5dacead2daf00e53c5e90d829ab5886fdd6289266381

View on Chainz ↗

Height

#243,227

Difficulty

9.961198

Transactions

Size

602 B

Version

Bits

09f61113

Nonce

7,782

Timestamp

11/4/2013, 4:25:59 AM

Confirmations

6,601,257

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

a34e39567a1b8692e85ccbb07a338a75950dc2348ab19518991d40fe2185aced

Transactions (2)

Coinbase487a29d919f61c…2217c8098fc9a3

1 in → 2 out10.0700 XPM137 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

56a8713b6391fa…ca48b4ea68e8da

2 in → 2 out18.0407 XPM373 B

AL1V8UeW…3xgbHEm9 ASuoUi24…FwBoFbxd

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.

1.785 × 10⁹⁹(100-digit number)

17852878101298968445…44681936589225011689

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

1.785 × 10⁹⁹(100-digit number)

17852878101298968445…44681936589225011689

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.785 × 10⁹⁹(100-digit number)

17852878101298968445…44681936589225011691

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

3.570 × 10⁹⁹(100-digit number)

35705756202597936891…89363873178450023379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.570 × 10⁹⁹(100-digit number)

35705756202597936891…89363873178450023381

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

7.141 × 10⁹⁹(100-digit number)

71411512405195873783…78727746356900046759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.141 × 10⁹⁹(100-digit number)

71411512405195873783…78727746356900046761

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

1.428 × 10¹⁰⁰(101-digit number)

14282302481039174756…57455492713800093519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.428 × 10¹⁰⁰(101-digit number)

14282302481039174756…57455492713800093521

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

2.856 × 10¹⁰⁰(101-digit number)

28564604962078349513…14910985427600187039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #243,227

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