Block #380,511

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 7:44:48 AM · Difficulty 10.4121 · 6,433,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86ff5ec517af6556c78b28626a48180794c6b124f356da18d181d82e59f91e8a

View on Chainz ↗

Height

#380,511

Difficulty

10.412146

Transactions

Size

1.87 KB

Version

Bits

0a69826e

Nonce

5,667

Timestamp

1/29/2014, 7:44:48 AM

Confirmations

6,433,374

Mined by

⛏️ _aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0720c4864bfae370aac85aac5245df22ea5080dfc80f47fe910569b194fc1837

Transactions (4)

Coinbasee21405eada231a…53895e819e1c1a

1 in → 20 out9.2100 XPM743 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 AZV4TwxQ…8JnQqSoH

4aa3a0f338df34…ab5e5a34c7b13e

3 in → 9 out27.5700 XPM659 B

AW6zyZju…feRjK7Un AUsL6VH6…Du8VQEdZ Aaxo3jsy…ei3XcWbn AZ3PWPr3…T7o8gD2E ALrZxq5u…jReX3z9e

fe8a3b9a748991…37982fcf0f634b

1 in → 1 out0.9962 XPM191 B

AYPynVaM…jhDK9x9m

db4d0cb14a8981…288289ff814f22

1 in → 2 out8.1531 XPM227 B

AcLDvygp…GAR414Po ASRUjjUX…eq2TdJaz

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.

4.293 × 10⁹⁵(96-digit number)

42938494672811213480…23912378471755290559

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

4.293 × 10⁹⁵(96-digit number)

42938494672811213480…23912378471755290559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.293 × 10⁹⁵(96-digit number)

42938494672811213480…23912378471755290561

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

8.587 × 10⁹⁵(96-digit number)

85876989345622426961…47824756943510581119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.587 × 10⁹⁵(96-digit number)

85876989345622426961…47824756943510581121

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

1.717 × 10⁹⁶(97-digit number)

17175397869124485392…95649513887021162239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.717 × 10⁹⁶(97-digit number)

17175397869124485392…95649513887021162241

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

3.435 × 10⁹⁶(97-digit number)

34350795738248970784…91299027774042324479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.435 × 10⁹⁶(97-digit number)

34350795738248970784…91299027774042324481

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

6.870 × 10⁹⁶(97-digit number)

68701591476497941569…82598055548084648959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.870 × 10⁹⁶(97-digit number)

68701591476497941569…82598055548084648961

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 #380,511

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