Block #473,669

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/4/2014, 2:01:24 AM · Difficulty 10.4462 · 6,341,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e13bb25da0c2b05cd90a0ef934d49f7a4692d0e715b059d2db04dcd308504f5

View on Chainz ↗

Height

#473,669

Difficulty

10.446152

Transactions

Size

2.58 KB

Version

Bits

0a723705

Nonce

584,432

Timestamp

4/4/2014, 2:01:24 AM

Confirmations

6,341,316

Mined by

⛏️ E:aS>wAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e20c0e24e0aa4899e0da6167f23fe0e457d7e289a0dc510f640497c5ae5a7e7a

Transactions (4)

Coinbase389338fabb05f0…2ec78e21831c4b

1 in → 23 out9.1500 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

0a3d55c67ad7b8…8f0a0e413df371

2 in → 2 out14.8362 XPM373 B

AJJu16ii…1zZTWnqc APBgmLKF…bFHjYYss

3676a01d366bb1…8a83de9dc671ff

7 in → 2 out49.0418 XPM1.09 KB

Aa1AvAie…Yv4xhXZC AYQvTCLi…wp1vbxM3

858398d5a24664…6c8e7311929ff9

1 in → 2 out7.0566 XPM227 B

AZ8ovUF9…6ugkpVtm ATygRnp8…mAEarLdh

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.

4.759 × 10⁹³(94-digit number)

47591201301355061933…51387154403573390039

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

4.759 × 10⁹³(94-digit number)

47591201301355061933…51387154403573390039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.759 × 10⁹³(94-digit number)

47591201301355061933…51387154403573390041

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

9.518 × 10⁹³(94-digit number)

95182402602710123867…02774308807146780079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.518 × 10⁹³(94-digit number)

95182402602710123867…02774308807146780081

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

1.903 × 10⁹⁴(95-digit number)

19036480520542024773…05548617614293560159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.903 × 10⁹⁴(95-digit number)

19036480520542024773…05548617614293560161

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

3.807 × 10⁹⁴(95-digit number)

38072961041084049547…11097235228587120319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.807 × 10⁹⁴(95-digit number)

38072961041084049547…11097235228587120321

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

7.614 × 10⁹⁴(95-digit number)

76145922082168099094…22194470457174240639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.614 × 10⁹⁴(95-digit number)

76145922082168099094…22194470457174240641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.522 × 10⁹⁵(96-digit number)

15229184416433619818…44388940914348481279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #473,669

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