Block #367,907

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 9:33:30 AM · Difficulty 10.4377 · 6,427,949 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07351a2e586d1b570fb994f4622f3d36af7fd30744d1b86c93cc710f9e8cd5d8

View on Chainz ↗

Height

#367,907

Difficulty

10.437654

Transactions

Size

1.54 KB

Version

Bits

0a700a12

Nonce

17,042

Timestamp

1/20/2014, 9:33:30 AM

Confirmations

6,427,949

Mined by

⛏️ #aRAHZUHC8gzgPMTvVe1nqY6FNTrht3rBwmSA

Merkle Root

88bc17feadde0f47d8ecd3ea9c27924926a372ea1b2b66f2876ecdcd6cfd71cd

Transactions (2)

Coinbaseb1cae66cb8e509…09f4cac975f8b8

1 in → 23 out9.1514 XPM845 B

AHZUHC8g…t3rBwmSA Ac5JXwCr…tf5C9dQa Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 ASAv2svc…JNebh6Lj

ad61506553ddb5…8128543ea1db52

4 in → 1 out12.4014 XPM637 B

AUx3SrnG…FtVUGsrD

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.

5.379 × 10¹⁰⁰(101-digit number)

53793422951877482318…51385510930503930879

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

5.379 × 10¹⁰⁰(101-digit number)

53793422951877482318…51385510930503930879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.379 × 10¹⁰⁰(101-digit number)

53793422951877482318…51385510930503930881

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

1.075 × 10¹⁰¹(102-digit number)

10758684590375496463…02771021861007861759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.075 × 10¹⁰¹(102-digit number)

10758684590375496463…02771021861007861761

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

2.151 × 10¹⁰¹(102-digit number)

21517369180750992927…05542043722015723519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.151 × 10¹⁰¹(102-digit number)

21517369180750992927…05542043722015723521

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

4.303 × 10¹⁰¹(102-digit number)

43034738361501985854…11084087444031447039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.303 × 10¹⁰¹(102-digit number)

43034738361501985854…11084087444031447041

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

8.606 × 10¹⁰¹(102-digit number)

86069476723003971709…22168174888062894079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.606 × 10¹⁰¹(102-digit number)

86069476723003971709…22168174888062894081

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