Block #185,486

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 8:20:37 AM · Difficulty 9.8622 · 6,623,801 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7f82a234bd81600ef72d296cf0ebdc9998f3c0202d16aecde5be221657a6f7e8

View on Chainz ↗

Height

#185,486

Difficulty

9.862206

Transactions

Size

1.31 KB

Version

Bits

09dcb989

Nonce

20,355

Timestamp

9/29/2013, 8:20:37 AM

Confirmations

6,623,801

Mined by

⛏️ P2SHAcDoNL3woMkoVVbfWWHitidKu9ViN23bk2

Merkle Root

9f0d7db9e4eae8296319877f30d69134b934854dce300ecb5e7c1cf6fc62e654

Transactions (3)

Coinbase43f3cbf57a647d…027789506c9b4e

1 in → 1 out10.2900 XPM109 B

AcDoNL3w…ViN23bk2

7581a02afbdd95…07d5cc5e073f4b

1 in → 4 out10.2600 XPM260 B

AbMXywDa…iBhmMkLU AFvfCa1W…3pZgbFWa AQXUSoBL…CzbjKp8b ALDjudvy…9PFfUsWu

916a8782564950…e89753495cf59f

5 in → 5 out15.6707 XPM884 B

AFvfCa1W…3pZgbFWa AUT1qxTx…t5B3qd8Z AQXUSoBL…CzbjKp8b AFuakYLn…xnY8QBEG AdWEcK3r…HNaeWgVb

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.

9.987 × 10⁹¹(92-digit number)

99876831494245907776…65174564634959958879

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

9.987 × 10⁹¹(92-digit number)

99876831494245907776…65174564634959958879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.987 × 10⁹¹(92-digit number)

99876831494245907776…65174564634959958881

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

1.997 × 10⁹²(93-digit number)

19975366298849181555…30349129269919917759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.997 × 10⁹²(93-digit number)

19975366298849181555…30349129269919917761

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

3.995 × 10⁹²(93-digit number)

39950732597698363110…60698258539839835519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.995 × 10⁹²(93-digit number)

39950732597698363110…60698258539839835521

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

7.990 × 10⁹²(93-digit number)

79901465195396726220…21396517079679671039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.990 × 10⁹²(93-digit number)

79901465195396726220…21396517079679671041

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

1.598 × 10⁹³(94-digit number)

15980293039079345244…42793034159359342079

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 #185,486

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