Block #474,220

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 10:46:16 AM · Difficulty 10.4489 · 6,336,098 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b75d6cc1b36f78de287ece4efcf330bf0c09ab6d6dcd6da39b5fa8b5d5361520

View on Chainz ↗

Height

#474,220

Difficulty

10.448867

Transactions

Size

1.46 KB

Version

Bits

0a72e8f1

Nonce

35,221

Timestamp

4/4/2014, 10:46:16 AM

Confirmations

6,336,098

Mined by

⛏️ l<aS>hZAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3620dc600a5e360d167f213479b03000683cc5f0ae3e5beafff176b9cd65a273

Transactions (2)

Coinbase4233e3ecc29587…56f9a9bb656c1f

1 in → 23 out9.1500 XPM845 B

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

4ad5318b479a8a…36637d0e1bc9bd

3 in → 4 out9.6120 XPM557 B

AeKNrjNj…1NEq95Ta AH6atPTv…Wc9ye5Jg AKc9Rmjx…Bir3N5mm AUfa5LFJ…C4BhhWGa

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.

1.094 × 10⁸⁹(90-digit number)

10940925624782905235…04690476249389038719

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

1.094 × 10⁸⁹(90-digit number)

10940925624782905235…04690476249389038719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.094 × 10⁸⁹(90-digit number)

10940925624782905235…04690476249389038721

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

2.188 × 10⁸⁹(90-digit number)

21881851249565810471…09380952498778077439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.188 × 10⁸⁹(90-digit number)

21881851249565810471…09380952498778077441

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

4.376 × 10⁸⁹(90-digit number)

43763702499131620943…18761904997556154879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.376 × 10⁸⁹(90-digit number)

43763702499131620943…18761904997556154881

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

8.752 × 10⁸⁹(90-digit number)

87527404998263241887…37523809995112309759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.752 × 10⁸⁹(90-digit number)

87527404998263241887…37523809995112309761

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

1.750 × 10⁹⁰(91-digit number)

17505480999652648377…75047619990224619519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.750 × 10⁹⁰(91-digit number)

17505480999652648377…75047619990224619521

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #474,220

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