Block #451,863

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/20/2014, 6:04:29 AM · Difficulty 10.3794 · 6,350,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cffbd96c5cc9631dd19f8a274a3023880dfb1ad28ff278b58a4bc4628cc7a74

View on Chainz ↗

Height

#451,863

Difficulty

10.379390

Transactions

Size

968 B

Version

Bits

0a611fb2

Nonce

26,595

Timestamp

3/20/2014, 6:04:29 AM

Confirmations

6,350,648

Mined by

⛏️ aS*8AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

cd870e0a99c703b1f10c17bacafa2b0767d85e5b8984a3cc9205cf14bd84eb14

Transactions (1)

Coinbasecd870e0a99c703…05cf14bd84eb14

1 in → 24 out9.2700 XPM879 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF AQ8QAT3J…rCFKuVbR AScAzqGc…BZ6tV1vJ AQyr8Lw3…hs4nt3Pn

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.

1.447 × 10⁹³(94-digit number)

14477660370518095694…59794535479427640959

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

1.447 × 10⁹³(94-digit number)

14477660370518095694…59794535479427640959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.447 × 10⁹³(94-digit number)

14477660370518095694…59794535479427640961

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

2.895 × 10⁹³(94-digit number)

28955320741036191389…19589070958855281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.895 × 10⁹³(94-digit number)

28955320741036191389…19589070958855281921

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

5.791 × 10⁹³(94-digit number)

57910641482072382778…39178141917710563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.791 × 10⁹³(94-digit number)

57910641482072382778…39178141917710563841

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

1.158 × 10⁹⁴(95-digit number)

11582128296414476555…78356283835421127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.158 × 10⁹⁴(95-digit number)

11582128296414476555…78356283835421127681

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

2.316 × 10⁹⁴(95-digit number)

23164256592828953111…56712567670842255359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.316 × 10⁹⁴(95-digit number)

23164256592828953111…56712567670842255361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.632 × 10⁹⁴(95-digit number)

46328513185657906222…13425135341684510719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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