Block #367,793

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 7:59:34 AM · Difficulty 10.4352 · 6,459,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7329d14ae152b711c2597ba56d50f166b0c67ce6c069148539be1bb5fb3fafb

View on Chainz ↗

Height

#367,793

Difficulty

10.435205

Transactions

Size

878 B

Version

Bits

0a6f699c

Nonce

85,320

Timestamp

1/20/2014, 7:59:34 AM

Confirmations

6,459,512

Mined by

⛏️ P2SHALkdwtZJ9NxLR6ndoRCSaJF5r4ZmXtwmhT

Merkle Root

6cc90717ac27a95c7120807e91ff931786c4cb7e8d87552db356cab7fef80be2

Transactions (4)

Coinbase26f57adaf998df…7b4b0b67ec8e2d

1 in → 1 out9.2000 XPM109 B

ALkdwtZJ…ZmXtwmhT

109faf69015d9e…cd245590aa7cfc

1 in → 2 out7.1585 XPM227 B

ATADmBFX…5jBQQUrH AGecNpfu…GTLQqkHB

eb38bade1a9bc7…2eaf1ede7c93dd

1 in → 2 out5.4404 XPM225 B

APaFJWfB…mWdBQT1i AXnL68UR…jsxeGUhN

63abb165c15dd3…e364b44a834093

1 in → 2 out3.0914 XPM226 B

AMU8nEj9…Eo32pqxr AY8MTxPp…rA6ZiNjV

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.

2.601 × 10⁹⁶(97-digit number)

26016272307363659063…18746044561857356199

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

2.601 × 10⁹⁶(97-digit number)

26016272307363659063…18746044561857356199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.601 × 10⁹⁶(97-digit number)

26016272307363659063…18746044561857356201

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

5.203 × 10⁹⁶(97-digit number)

52032544614727318127…37492089123714712399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.203 × 10⁹⁶(97-digit number)

52032544614727318127…37492089123714712401

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

1.040 × 10⁹⁷(98-digit number)

10406508922945463625…74984178247429424799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.040 × 10⁹⁷(98-digit number)

10406508922945463625…74984178247429424801

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

2.081 × 10⁹⁷(98-digit number)

20813017845890927251…49968356494858849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.081 × 10⁹⁷(98-digit number)

20813017845890927251…49968356494858849601

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

4.162 × 10⁹⁷(98-digit number)

41626035691781854502…99936712989717699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.162 × 10⁹⁷(98-digit number)

41626035691781854502…99936712989717699201

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 #367,793

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