Block #336,456

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 11:33:20 PM · Difficulty 10.1416 · 6,473,327 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4046e0a3c38dd8342d94df4ee268c65a27b1817deeb24912e3422ad8d0985e75

View on Chainz ↗

Height

#336,456

Difficulty

10.141581

Transactions

Size

1.20 KB

Version

Bits

0a243eaa

Nonce

454,418

Timestamp

12/30/2013, 11:33:20 PM

Confirmations

6,473,327

Mined by

⛏️ H"aR,AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

b83542a5eb72089fed127f0210cb4c6af10e9ccc85151752096ec2a9d4123b88

Transactions (2)

Coinbase73177f503630c0…e75e20fc36a094

1 in → 25 out9.7100 XPM913 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AYtDvcGs…VuAcA7m7

e064be6bfd64a7…9441102a6ad47b

1 in → 2 out1.2244 XPM226 B

AaQpPLpu…ommbU2nz AbVF4xCa…fDtmHqLZ

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.

6.244 × 10⁹¹(92-digit number)

62447735747954398101…53629789929753165679

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

6.244 × 10⁹¹(92-digit number)

62447735747954398101…53629789929753165679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.244 × 10⁹¹(92-digit number)

62447735747954398101…53629789929753165681

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

1.248 × 10⁹²(93-digit number)

12489547149590879620…07259579859506331359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.248 × 10⁹²(93-digit number)

12489547149590879620…07259579859506331361

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

2.497 × 10⁹²(93-digit number)

24979094299181759240…14519159719012662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.497 × 10⁹²(93-digit number)

24979094299181759240…14519159719012662721

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

4.995 × 10⁹²(93-digit number)

49958188598363518481…29038319438025325439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.995 × 10⁹²(93-digit number)

49958188598363518481…29038319438025325441

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

9.991 × 10⁹²(93-digit number)

99916377196727036962…58076638876050650879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.991 × 10⁹²(93-digit number)

99916377196727036962…58076638876050650881

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 #336,456

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