Block #215,685

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 6:25:27 AM · Difficulty 9.9254 · 6,600,940 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d207f6ff4472bc684c475ac543240daa9e589e263f3a0502459512ae16bcf98

View on Chainz ↗

Height

#215,685

Difficulty

9.925396

Transactions

Size

3.27 KB

Version

Bits

09ece6c4

Nonce

40,957

Timestamp

10/18/2013, 6:25:27 AM

Confirmations

6,600,940

Mined by

⛏️ JR`M}AXx8WhsNAFDPw8gGrLzZNtV8uJi5uHr3Yv

Merkle Root

d5befb3bf7eb522729d50d0b3221ab38f954dfe664da39bb243e9f952ee8a4c4

Transactions (1)

Coinbased5befb3bf7eb52…3e9f952ee8a4c4

1 in → 94 out10.0967 XPM3.18 KB

AXx8WhsN…i5uHr3Yv AbdqpFgm…M8UVG4YE AHY1L1zP…op3KHdyK AeoxjYiE…9nSkGjFC AFuakYLn…xnY8QBEG

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.

1.105 × 10⁹³(94-digit number)

11057882907944148550…18379725614803969919

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

1.105 × 10⁹³(94-digit number)

11057882907944148550…18379725614803969919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.105 × 10⁹³(94-digit number)

11057882907944148550…18379725614803969921

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

2.211 × 10⁹³(94-digit number)

22115765815888297100…36759451229607939839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.211 × 10⁹³(94-digit number)

22115765815888297100…36759451229607939841

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

4.423 × 10⁹³(94-digit number)

44231531631776594201…73518902459215879679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.423 × 10⁹³(94-digit number)

44231531631776594201…73518902459215879681

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

8.846 × 10⁹³(94-digit number)

88463063263553188402…47037804918431759359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.846 × 10⁹³(94-digit number)

88463063263553188402…47037804918431759361

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

1.769 × 10⁹⁴(95-digit number)

17692612652710637680…94075609836863518719

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 #215,685

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