Block #264,624

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/18/2013, 8:55:22 PM · Difficulty 9.9640 · 6,544,093 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

063e05b021adfe9e6b913e8c309a369719d15c83048cd66d6fd18b0572bbf348

View on Chainz ↗

Height

#264,624

Difficulty

9.963992

Transactions

Size

826 B

Version

Bits

09f6c831

Nonce

10,735

Timestamp

11/18/2013, 8:55:22 PM

Confirmations

6,544,093

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

9bb26c199c5b6764c95359b8dc5e045684d20001ea88cf3ec3b29d09b9324929

Transactions (3)

Coinbase9d11f8ab1e766b…745453432ea660

1 in → 2 out10.0800 XPM136 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

cbdd8c04533ec1…cda5167b4a7335

1 in → 1 out499.9900 XPM192 B

AabgMQz4…UKoARTNg

1830861d011a25…81c1f00853b9a6

2 in → 4 out10.7634 XPM408 B

ALTYmdso…QJTNXbLm AeKNrjNj…1NEq95Ta AeuvG87z…Dq9vhgX9 AMuPGPXT…eMMNvd8v

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.

6.382 × 10⁹⁴(95-digit number)

63825042720696521544…27630999274062304799

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

6.382 × 10⁹⁴(95-digit number)

63825042720696521544…27630999274062304799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.382 × 10⁹⁴(95-digit number)

63825042720696521544…27630999274062304801

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

1.276 × 10⁹⁵(96-digit number)

12765008544139304308…55261998548124609599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.276 × 10⁹⁵(96-digit number)

12765008544139304308…55261998548124609601

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

2.553 × 10⁹⁵(96-digit number)

25530017088278608617…10523997096249219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.553 × 10⁹⁵(96-digit number)

25530017088278608617…10523997096249219201

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

5.106 × 10⁹⁵(96-digit number)

51060034176557217235…21047994192498438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.106 × 10⁹⁵(96-digit number)

51060034176557217235…21047994192498438401

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

1.021 × 10⁹⁶(97-digit number)

10212006835311443447…42095988384996876799

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 #264,624

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