Block #437,926

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 3:26:26 PM · Difficulty 10.3596 · 6,389,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb4164f72872884d5f7d8750b04e378ab6f6734562789810495758c36bdb22c6

View on Chainz ↗

Height

#437,926

Difficulty

10.359568

Transactions

Size

1.08 KB

Version

Bits

0a5c0c9f

Nonce

5,045

Timestamp

3/10/2014, 3:26:26 PM

Confirmations

6,389,126

Mined by

⛏️ P2SHAVcFrpvFviUNPhi8SjoKPnpX5xc6FPYDaF

Merkle Root

e80a1dff8546ba2216790a3f893feb6fc6bf43e191ca5ddaf70b65eb20279300

Transactions (5)

Coinbasec976f58c48462b…a9995797bdfe01

1 in → 1 out9.3400 XPM109 B

AVcFrpvF…c6FPYDaF

9877e2d5a0366f…8f487c1e25c20b

1 in → 2 out8.2073 XPM226 B

AaVnd82B…X2x3WMeC AJC1C9RX…dXN1bFni

faf161bd867e09…faa381cdab12f3

1 in → 2 out6.6570 XPM227 B

AH5z2N4o…rt3rTtAF AVYWpamp…3Xtz41QK

20ce7a2a475846…1a344ae9c82568

1 in → 2 out3.1924 XPM226 B

AQFGQr2c…dscttDRG AGvJopN6…X8FKNDM6

aa2b21c8f1b395…c488b50395f445

1 in → 2 out1.6289 XPM227 B

APFsQ3Fo…xoFKrF12 AM7PUz3h…ihP5ZRFn

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.

2.258 × 10⁹⁴(95-digit number)

22583406565389642675…24831085133546466559

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

2.258 × 10⁹⁴(95-digit number)

22583406565389642675…24831085133546466559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.258 × 10⁹⁴(95-digit number)

22583406565389642675…24831085133546466561

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

4.516 × 10⁹⁴(95-digit number)

45166813130779285350…49662170267092933119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.516 × 10⁹⁴(95-digit number)

45166813130779285350…49662170267092933121

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

9.033 × 10⁹⁴(95-digit number)

90333626261558570701…99324340534185866239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.033 × 10⁹⁴(95-digit number)

90333626261558570701…99324340534185866241

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

1.806 × 10⁹⁵(96-digit number)

18066725252311714140…98648681068371732479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.806 × 10⁹⁵(96-digit number)

18066725252311714140…98648681068371732481

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

3.613 × 10⁹⁵(96-digit number)

36133450504623428280…97297362136743464959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.613 × 10⁹⁵(96-digit number)

36133450504623428280…97297362136743464961

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 #437,926

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