Block #429,232

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 3:35:24 PM · Difficulty 10.3466 · 6,379,769 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e2694e49d4be3135c7f55177d74e7665c45849244193bb39926e478adc53682

View on Chainz ↗

Height

#429,232

Difficulty

10.346569

Transactions

Size

1.08 KB

Version

Bits

0a58b8bf

Nonce

50,050

Timestamp

3/4/2014, 3:35:24 PM

Confirmations

6,379,769

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b105d79834fb4d369c20ae6145ee6cbd3493a3aa3e1db32b5ab52ef687bbf9ec

Transactions (5)

Coinbase2b076786e39b14…5b3780e508c2b3

1 in → 1 out9.3700 XPM116 B

AbwWkWZt…kawDhufa

f38e1edae9eb48…350f69c720eea3

1 in → 2 out9.2000 XPM227 B

AZTqUZRh…MVU9PKSd AGJN7GuY…RpZmsneu

44cf31990675a1…6391e3677649e6

1 in → 2 out8.1881 XPM226 B

ANDB2HhY…yL6QcBNm AdVfMywc…HbVLAgsY

294c2e7a9dc527…cfb48b01b01d44

1 in → 2 out7.1755 XPM225 B

AUH8H7bo…LBL5P3tp ARTBJrp3…KtyfiStG

6756d9a0dc52b5…45a40f627a5f84

1 in → 2 out3.1093 XPM226 B

AGyhc9Ym…YqF23X8n AG6cucXq…ynCh1TkM

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.

2.365 × 10⁹³(94-digit number)

23656773167901151130…18420200972099793279

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

2.365 × 10⁹³(94-digit number)

23656773167901151130…18420200972099793279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.365 × 10⁹³(94-digit number)

23656773167901151130…18420200972099793281

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

4.731 × 10⁹³(94-digit number)

47313546335802302261…36840401944199586559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.731 × 10⁹³(94-digit number)

47313546335802302261…36840401944199586561

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

9.462 × 10⁹³(94-digit number)

94627092671604604522…73680803888399173119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.462 × 10⁹³(94-digit number)

94627092671604604522…73680803888399173121

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

1.892 × 10⁹⁴(95-digit number)

18925418534320920904…47361607776798346239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.892 × 10⁹⁴(95-digit number)

18925418534320920904…47361607776798346241

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

3.785 × 10⁹⁴(95-digit number)

37850837068641841809…94723215553596692479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.785 × 10⁹⁴(95-digit number)

37850837068641841809…94723215553596692481

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 #429,232

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