Block #379,540

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 2:34:57 PM · Difficulty 10.4188 · 6,428,371 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e729d631169a42563f7c7f82f9cf745592a5564fe925419118fe2113217df260

View on Chainz ↗

Height

#379,540

Difficulty

10.418843

Transactions

Size

1.69 KB

Version

Bits

0a6b394d

Nonce

4,063

Timestamp

1/28/2014, 2:34:57 PM

Confirmations

6,428,371

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ee88890730eaf8a0e2cca7a933d179e12adf6511695af97152cead49e945d4aa

Transactions (2)

Coinbase18a70eec9b4e99…9704578a944675

1 in → 24 out9.2000 XPM879 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF ARyioPoT…UiofHnMr ALzmfS5h…pGPavftE AGKhfQo2…h7fBXLX6

46cf6a5401a2fc…cedc9baf96325d

6 in → 1 out46.8182 XPM762 B

AJjEKveq…Ldtq9FLd

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.

2.410 × 10⁹²(93-digit number)

24104227709814095132…84078453073661807999

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

2.410 × 10⁹²(93-digit number)

24104227709814095132…84078453073661807999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.410 × 10⁹²(93-digit number)

24104227709814095132…84078453073661808001

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

4.820 × 10⁹²(93-digit number)

48208455419628190264…68156906147323615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.820 × 10⁹²(93-digit number)

48208455419628190264…68156906147323616001

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

9.641 × 10⁹²(93-digit number)

96416910839256380528…36313812294647231999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.641 × 10⁹²(93-digit number)

96416910839256380528…36313812294647232001

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

1.928 × 10⁹³(94-digit number)

19283382167851276105…72627624589294463999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.928 × 10⁹³(94-digit number)

19283382167851276105…72627624589294464001

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

3.856 × 10⁹³(94-digit number)

38566764335702552211…45255249178588927999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.856 × 10⁹³(94-digit number)

38566764335702552211…45255249178588928001

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 #379,540

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