Block #478,217

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 10:48:06 PM · Difficulty 10.4914 · 6,331,279 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02f4b848cdc3be4633f6790eaf204773153f32c413115179e607822ca20314b2

View on Chainz ↗

Height

#478,217

Difficulty

10.491403

Transactions

Size

937 B

Version

Bits

0a7dcc93

Nonce

54,092

Timestamp

4/6/2014, 10:48:06 PM

Confirmations

6,331,279

Mined by

⛏️ L%cAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

bc24e586f8d33f98ffa293a2c625893096c621f7de8a80a67f3b170e85b6f32d

Transactions (1)

Coinbasebc24e586f8d33f…3b170e85b6f32d

1 in → 23 out9.0700 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AZ34NcPy…8FPeFjPV AMW1p9oT…2TzdaZxH

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.

2.781 × 10⁹⁸(99-digit number)

27819391705025070547…29641133378000456319

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

2.781 × 10⁹⁸(99-digit number)

27819391705025070547…29641133378000456319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.781 × 10⁹⁸(99-digit number)

27819391705025070547…29641133378000456321

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

5.563 × 10⁹⁸(99-digit number)

55638783410050141094…59282266756000912639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.563 × 10⁹⁸(99-digit number)

55638783410050141094…59282266756000912641

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

1.112 × 10⁹⁹(100-digit number)

11127756682010028218…18564533512001825279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.112 × 10⁹⁹(100-digit number)

11127756682010028218…18564533512001825281

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

2.225 × 10⁹⁹(100-digit number)

22255513364020056437…37129067024003650559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.225 × 10⁹⁹(100-digit number)

22255513364020056437…37129067024003650561

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

4.451 × 10⁹⁹(100-digit number)

44511026728040112875…74258134048007301119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.451 × 10⁹⁹(100-digit number)

44511026728040112875…74258134048007301121

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 #478,217

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