Block #376,012

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2014, 3:10:52 AM · Difficulty 10.4224 · 6,434,567 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f9b5fda7e4be59ea9bf527b3baf4b2123189905a1413ff3cd2405374fba1063

View on Chainz ↗

Height

#376,012

Difficulty

10.422416

Transactions

Size

1.87 KB

Version

Bits

0a6c2370

Nonce

242,892

Timestamp

1/26/2014, 3:10:52 AM

Confirmations

6,434,567

Mined by

⛏️ aR|qAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

562e07c687296cd4c467d2a512a85266d68c4abdcc7a7a37052da0d38c46f6cd

Transactions (4)

Coinbase2f0e4c83bfe3c1…37d318537f4dd8

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ARYJiGcH…7eaSxdkL AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6

970c6a66fa1cf1…c8c2e57c328343

3 in → 1 out2.0000 XPM488 B

AYvJFuS7…soXooeap

6103146658436f…9b341293e659aa

1 in → 2 out4.2851 XPM227 B

AZcLEz9j…p5iH6pLW AXxp24rY…yi3yUFBu

c8af29dd195b35…f8f8b539967a44

1 in → 2 out3.2973 XPM226 B

AMC6L9F1…ptWTJfeK AaaXC6Pb…TyNrJT7w

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.

1.471 × 10⁹⁷(98-digit number)

14711046528771730701…34691781837097640959

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

1.471 × 10⁹⁷(98-digit number)

14711046528771730701…34691781837097640959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.471 × 10⁹⁷(98-digit number)

14711046528771730701…34691781837097640961

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

2.942 × 10⁹⁷(98-digit number)

29422093057543461402…69383563674195281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.942 × 10⁹⁷(98-digit number)

29422093057543461402…69383563674195281921

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

5.884 × 10⁹⁷(98-digit number)

58844186115086922805…38767127348390563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.884 × 10⁹⁷(98-digit number)

58844186115086922805…38767127348390563841

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

1.176 × 10⁹⁸(99-digit number)

11768837223017384561…77534254696781127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.176 × 10⁹⁸(99-digit number)

11768837223017384561…77534254696781127681

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

2.353 × 10⁹⁸(99-digit number)

23537674446034769122…55068509393562255359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.353 × 10⁹⁸(99-digit number)

23537674446034769122…55068509393562255361

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 #376,012

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