Block #412,264

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/20/2014, 9:58:36 AM · Difficulty 10.4177 · 6,397,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c914636e8f180d37c10b29e8b41458c1bff7010ef5e1b2b1c80f3d79667d71bd

View on Chainz ↗

Height

#412,264

Difficulty

10.417708

Transactions

Size

835 B

Version

Bits

0a6aeeec

Nonce

165,057

Timestamp

2/20/2014, 9:58:36 AM

Confirmations

6,397,191

Mined by

⛏️ hJaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

fea21fade418aca7d258f51daff598b07fff01d2dc60fb50883e4cec09ba5ae4

Transactions (1)

Coinbasefea21fade418ac…3e4cec09ba5ae4

1 in → 20 out9.2000 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

1.695 × 10⁹⁹(100-digit number)

16951025002389825044…47177410708721976319

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

1.695 × 10⁹⁹(100-digit number)

16951025002389825044…47177410708721976319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.695 × 10⁹⁹(100-digit number)

16951025002389825044…47177410708721976321

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

3.390 × 10⁹⁹(100-digit number)

33902050004779650088…94354821417443952639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.390 × 10⁹⁹(100-digit number)

33902050004779650088…94354821417443952641

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

6.780 × 10⁹⁹(100-digit number)

67804100009559300177…88709642834887905279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.780 × 10⁹⁹(100-digit number)

67804100009559300177…88709642834887905281

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

1.356 × 10¹⁰⁰(101-digit number)

13560820001911860035…77419285669775810559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.356 × 10¹⁰⁰(101-digit number)

13560820001911860035…77419285669775810561

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

2.712 × 10¹⁰⁰(101-digit number)

27121640003823720071…54838571339551621119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.712 × 10¹⁰⁰(101-digit number)

27121640003823720071…54838571339551621121

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 #412,264

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