Block #551,190

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2014, 4:10:14 PM · Difficulty 10.9621 · 6,261,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aed05393767cde83f7405c4aa9c5d625508c79f720d119a98175e662c2b2d089

View on Chainz ↗

Height

#551,190

Difficulty

10.962094

Transactions

Size

697 B

Version

Bits

0af64bc4

Nonce

137,574

Timestamp

5/18/2014, 4:10:14 PM

Confirmations

6,261,368

Mined by

⛏️ iaSxIlAHwvxqCNvsnPA75eepHf4rKFfZ7z7foF67

Merkle Root

6437edd18706e25b0cd213bfdd37ae0599b1782225eb35ff26cc5c85e51b4807

Transactions (1)

Coinbase6437edd18706e2…cc5c85e51b4807

1 in → 16 out8.3100 XPM606 B

AHwvxqCN…7z7foF67 AQv2iMwd…EFna22ee AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q AQvZBsUo…hppgRZTJ

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.

3.683 × 10⁹⁶(97-digit number)

36834801265380605696…41578994230233913939

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

3.683 × 10⁹⁶(97-digit number)

36834801265380605696…41578994230233913939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.683 × 10⁹⁶(97-digit number)

36834801265380605696…41578994230233913941

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

7.366 × 10⁹⁶(97-digit number)

73669602530761211392…83157988460467827879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.366 × 10⁹⁶(97-digit number)

73669602530761211392…83157988460467827881

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

1.473 × 10⁹⁷(98-digit number)

14733920506152242278…66315976920935655759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.473 × 10⁹⁷(98-digit number)

14733920506152242278…66315976920935655761

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

2.946 × 10⁹⁷(98-digit number)

29467841012304484557…32631953841871311519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.946 × 10⁹⁷(98-digit number)

29467841012304484557…32631953841871311521

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

5.893 × 10⁹⁷(98-digit number)

58935682024608969114…65263907683742623039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.893 × 10⁹⁷(98-digit number)

58935682024608969114…65263907683742623041

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

1.178 × 10⁹⁸(99-digit number)

11787136404921793822…30527815367485246079

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

Block #551,190

Cookie Preferences