Block #368,591

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 8:11:42 PM · Difficulty 10.4427 · 6,439,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fa2e34d7f548e0edda2a35fa605261efdfbea7418b13a02400813e673ee78e5

View on Chainz ↗

Height

#368,591

Difficulty

10.442683

Transactions

Size

1.66 KB

Version

Bits

0a7153a4

Nonce

78,912

Timestamp

1/20/2014, 8:11:42 PM

Confirmations

6,439,418

Mined by

⛏️ P2SHAewiA1hrUH8uiA2X41i9DEP5BbtCL2j8Cj

Merkle Root

934880b97a41de3facb62c85efeffa02c06ecff32a4ea9ca1309bad9d57cda8e

Transactions (5)

Coinbasebe4a5c5e5684cf…056d26330468c3

1 in → 1 out9.2000 XPM109 B

AewiA1hr…tCL2j8Cj

13fa1e4a5e2d63…ccc92d6a8c9570

1 in → 2 out5.0266 XPM226 B

AQf4KwjF…MNYQAorr AKGAx88N…3Aqww7sm

7ce8f8d9b1c8fd…b313f7cb253d58

1 in → 2 out4.0692 XPM227 B

AVr2THVi…md6YFBDH AHFkDvKn…k9HLQgdY

c2b99af3b16e13…20f872323d1509

1 in → 2 out2.3260 XPM227 B

ARFYamUb…rvdijap8 Acfn2qFR…FDGoTvxd

23b554f5506146…e3f91fe304b110

5 in → 2 out2.0141 XPM818 B

AKSPEYem…8QKhFRe6 AcyQ527q…3jADZ8MP

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.

5.756 × 10⁹³(94-digit number)

57567492177166901133…84945241456014285599

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

5.756 × 10⁹³(94-digit number)

57567492177166901133…84945241456014285599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.756 × 10⁹³(94-digit number)

57567492177166901133…84945241456014285601

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

1.151 × 10⁹⁴(95-digit number)

11513498435433380226…69890482912028571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.151 × 10⁹⁴(95-digit number)

11513498435433380226…69890482912028571201

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

2.302 × 10⁹⁴(95-digit number)

23026996870866760453…39780965824057142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.302 × 10⁹⁴(95-digit number)

23026996870866760453…39780965824057142401

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

4.605 × 10⁹⁴(95-digit number)

46053993741733520907…79561931648114284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.605 × 10⁹⁴(95-digit number)

46053993741733520907…79561931648114284801

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

9.210 × 10⁹⁴(95-digit number)

92107987483467041814…59123863296228569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.210 × 10⁹⁴(95-digit number)

92107987483467041814…59123863296228569601

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 #368,591

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