Block #377,937

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 11:37:25 AM · Difficulty 10.4202 · 6,421,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9da6b4e8f0ad8b6d5cbbd2dbd0ec62586d7df3671266417e2c99065b00aafafe

View on Chainz ↗

Height

#377,937

Difficulty

10.420229

Transactions

Size

1.28 KB

Version

Bits

0a6b9428

Nonce

132,365

Timestamp

1/27/2014, 11:37:25 AM

Confirmations

6,421,316

Mined by

⛏️ QaRDJAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

61150323f87303ece881244a3c7178c0f2df87198d2c951439e25ca7a73854ce

Transactions (2)

Coinbase3efd823d9eb51e…8a4cce9796bca2

1 in → 22 out9.2000 XPM811 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH ARYJiGcH…7eaSxdkL AGQxR1oS…2N1xAZXN

8310da60150bd9…9c83cc93bc260b

2 in → 4 out9.4437 XPM410 B

APGhKKy1…axmZARuS AMMSpxFF…5AwmfBJ2 AZH3aBJB…T7FVgZ83 AeKNrjNj…1NEq95Ta

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.

3.688 × 10⁹²(93-digit number)

36888901392854845784…54058660039714778599

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

3.688 × 10⁹²(93-digit number)

36888901392854845784…54058660039714778599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.688 × 10⁹²(93-digit number)

36888901392854845784…54058660039714778601

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

7.377 × 10⁹²(93-digit number)

73777802785709691568…08117320079429557199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.377 × 10⁹²(93-digit number)

73777802785709691568…08117320079429557201

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

1.475 × 10⁹³(94-digit number)

14755560557141938313…16234640158859114399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.475 × 10⁹³(94-digit number)

14755560557141938313…16234640158859114401

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

2.951 × 10⁹³(94-digit number)

29511121114283876627…32469280317718228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.951 × 10⁹³(94-digit number)

29511121114283876627…32469280317718228801

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

5.902 × 10⁹³(94-digit number)

59022242228567753254…64938560635436457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.902 × 10⁹³(94-digit number)

59022242228567753254…64938560635436457601

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