Block #437,365

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 6:17:32 AM · Difficulty 10.3578 · 6,379,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ad343d44a2125205184b5ab346635bb2203a07188f87d6d7686ca6fb170c1b3

View on Chainz ↗

Height

#437,365

Difficulty

10.357805

Transactions

Size

1003 B

Version

Bits

0a5b9915

Nonce

648,124

Timestamp

3/10/2014, 6:17:32 AM

Confirmations

6,379,994

Mined by

⛏️ uaSXTAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c7d9a912d6386e17e20b968e951d1f61254bcba984d261f0fb05c78b41a09f81

Transactions (1)

Coinbasec7d9a912d6386e…05c78b41a09f81

1 in → 25 out9.3100 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ

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.

2.028 × 10⁹⁴(95-digit number)

20280261947735957149…69628325174739476479

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

2.028 × 10⁹⁴(95-digit number)

20280261947735957149…69628325174739476479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.028 × 10⁹⁴(95-digit number)

20280261947735957149…69628325174739476481

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

4.056 × 10⁹⁴(95-digit number)

40560523895471914299…39256650349478952959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.056 × 10⁹⁴(95-digit number)

40560523895471914299…39256650349478952961

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

8.112 × 10⁹⁴(95-digit number)

81121047790943828599…78513300698957905919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.112 × 10⁹⁴(95-digit number)

81121047790943828599…78513300698957905921

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

1.622 × 10⁹⁵(96-digit number)

16224209558188765719…57026601397915811839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.622 × 10⁹⁵(96-digit number)

16224209558188765719…57026601397915811841

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

3.244 × 10⁹⁵(96-digit number)

32448419116377531439…14053202795831623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.244 × 10⁹⁵(96-digit number)

32448419116377531439…14053202795831623681

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 #437,365

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