Block #66,261

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 4:32:45 PM · Difficulty 8.9858 · 6,733,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ad481354a79cc0bc446496f19846c8e72b501bc170e02d93bf2ff6a77c53372

View on Chainz ↗

Height

#66,261

Difficulty

8.985839

Transactions

Size

1.21 KB

Version

Bits

08fc5ff1

Nonce

Timestamp

7/19/2013, 4:32:45 PM

Confirmations

6,733,000

Mined by

⛏️ P2SHAR7YzWnhfbhjMa7cwKHK7T8ECFXPVGCnjf

Merkle Root

7eb61d21fb1049344b90969109e6de98bf63f2910fb68c8ab98ae95002c286b6

Transactions (3)

Coinbase1167534aa00be4…5f209ca7a6d066

1 in → 1 out12.3900 XPM110 B

AR7YzWnh…XPVGCnjf

9b0a999f58d749…72fb79417fbc75

3 in → 2 out136.1903 XPM522 B

AeASzLHG…foyFKTA8 AQnNKxxD…xyvGpsKY

486b0d94906a74…4433c069b59c3e

3 in → 2 out289.0203 XPM522 B

AHiWRfVb…4sZjZf6j AW7aqm7z…MZ7TogRx

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.

1.512 × 10⁸⁸(89-digit number)

15125354672812355523…56787783745783007229

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

1.512 × 10⁸⁸(89-digit number)

15125354672812355523…56787783745783007229

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.512 × 10⁸⁸(89-digit number)

15125354672812355523…56787783745783007231

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

3.025 × 10⁸⁸(89-digit number)

30250709345624711046…13575567491566014459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.025 × 10⁸⁸(89-digit number)

30250709345624711046…13575567491566014461

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

6.050 × 10⁸⁸(89-digit number)

60501418691249422092…27151134983132028919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.050 × 10⁸⁸(89-digit number)

60501418691249422092…27151134983132028921

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

1.210 × 10⁸⁹(90-digit number)

12100283738249884418…54302269966264057839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.210 × 10⁸⁹(90-digit number)

12100283738249884418…54302269966264057841

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

2.420 × 10⁸⁹(90-digit number)

24200567476499768837…08604539932528115679

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