Block #483,972

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 8:07:26 AM · Difficulty 10.5746 · 6,317,021 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22912bae802ee906da0ceb0e2e5f58f6d160f4cd2b7fe029df62dcc6d06a1a34

View on Chainz ↗

Height

#483,972

Difficulty

10.574594

Transactions

Size

937 B

Version

Bits

0a931897

Nonce

55,974

Timestamp

4/10/2014, 8:07:26 AM

Confirmations

6,317,021

Mined by

⛏️ baSFQ'0AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

92aa87f64eeda5e5b7c6af5d57707a1fc3dd0ce57f8a1092a7475558632b513b

Transactions (1)

Coinbase92aa87f64eeda5…475558632b513b

1 in → 23 out8.9300 XPM845 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1

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.

1.903 × 10⁹⁸(99-digit number)

19039075329170593887…63615813587207484799

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

1.903 × 10⁹⁸(99-digit number)

19039075329170593887…63615813587207484799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.903 × 10⁹⁸(99-digit number)

19039075329170593887…63615813587207484801

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

3.807 × 10⁹⁸(99-digit number)

38078150658341187774…27231627174414969599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.807 × 10⁹⁸(99-digit number)

38078150658341187774…27231627174414969601

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

7.615 × 10⁹⁸(99-digit number)

76156301316682375548…54463254348829939199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.615 × 10⁹⁸(99-digit number)

76156301316682375548…54463254348829939201

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

1.523 × 10⁹⁹(100-digit number)

15231260263336475109…08926508697659878399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.523 × 10⁹⁹(100-digit number)

15231260263336475109…08926508697659878401

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

3.046 × 10⁹⁹(100-digit number)

30462520526672950219…17853017395319756799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.046 × 10⁹⁹(100-digit number)

30462520526672950219…17853017395319756801

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