Block #396,615

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 12:20:36 PM · Difficulty 10.4148 · 6,397,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c06eccbbdf7d398678dd33c414122585a601b043044e76ebc88de711202ef92

View on Chainz ↗

Height

#396,615

Difficulty

10.414823

Transactions

Size

1.80 KB

Version

Bits

0a6a31d7

Nonce

46,632

Timestamp

2/9/2014, 12:20:36 PM

Confirmations

6,397,738

Merkle Root

e787160de21a9780a7f1a5372d406fd37263b7a7b385912f687dd33183d0bc63

Transactions (4)

Coinbase195da2df32bca5…7b6ba2907f8837

1 in → 21 out9.2100 XPM777 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

7dd5201afb163d…b0f48f763618ce

2 in → 2 out16.3500 XPM373 B

APaSkzEP…e9f176Qr AQfApxRc…pCGdiTT6

c0dca28edd2ca9…858dffaad5017b

2 in → 2 out11.5580 XPM372 B

AbWa1SNW…cV3NPmGs AUnJWdJf…4HYNqFnQ

86f888396a0a98…aeef8a191139f6

1 in → 2 out8.0518 XPM225 B

AMbWEZH9…5QzQwJTw Ae6B2Grq…6ttkvNvc

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.

1.833 × 10⁹⁹(100-digit number)

18334836029899275237…11317783826953702399

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

1.833 × 10⁹⁹(100-digit number)

18334836029899275237…11317783826953702399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.833 × 10⁹⁹(100-digit number)

18334836029899275237…11317783826953702401

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

3.666 × 10⁹⁹(100-digit number)

36669672059798550475…22635567653907404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.666 × 10⁹⁹(100-digit number)

36669672059798550475…22635567653907404801

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

7.333 × 10⁹⁹(100-digit number)

73339344119597100951…45271135307814809599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.333 × 10⁹⁹(100-digit number)

73339344119597100951…45271135307814809601

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

1.466 × 10¹⁰⁰(101-digit number)

14667868823919420190…90542270615629619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.466 × 10¹⁰⁰(101-digit number)

14667868823919420190…90542270615629619201

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

2.933 × 10¹⁰⁰(101-digit number)

29335737647838840380…81084541231259238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.933 × 10¹⁰⁰(101-digit number)

29335737647838840380…81084541231259238401

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