Block #442,871

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 4:16:07 AM · Difficulty 10.3435 · 6,348,068 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2c556e7d46603613f03921ff14e08df4381ad96715e69c6c9d5c8508a00332f

View on Chainz ↗

Height

#442,871

Difficulty

10.343458

Transactions

Size

684 B

Version

Bits

0a57ece0

Nonce

2,944

Timestamp

3/14/2014, 4:16:07 AM

Confirmations

6,348,068

Merkle Root

3823c21b06d0a422aaf39a68d5425781ec072dfe788dd9ef6a8902a23fe6b7e5

Transactions (2)

Coinbase659545ba6f14bc…03737d271280b0

1 in → 1 out9.3400 XPM116 B

AbwWkWZt…kawDhufa

5e41d213508a51…be466ce3ec86e9

2 in → 7 out18.6000 XPM476 B

AVrD6maY…W77cdqzz AcGCmc9D…1fUXRBUx AR7BsVgY…cBPcAhhF AKy4P26p…bxEZW13i AeKNrjNj…1NEq95Ta

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.

1.869 × 10⁹⁸(99-digit number)

18691265848734574151…26475596836930949119

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

1.869 × 10⁹⁸(99-digit number)

18691265848734574151…26475596836930949119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.869 × 10⁹⁸(99-digit number)

18691265848734574151…26475596836930949121

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

3.738 × 10⁹⁸(99-digit number)

37382531697469148303…52951193673861898239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.738 × 10⁹⁸(99-digit number)

37382531697469148303…52951193673861898241

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

7.476 × 10⁹⁸(99-digit number)

74765063394938296606…05902387347723796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.476 × 10⁹⁸(99-digit number)

74765063394938296606…05902387347723796481

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

1.495 × 10⁹⁹(100-digit number)

14953012678987659321…11804774695447592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.495 × 10⁹⁹(100-digit number)

14953012678987659321…11804774695447592961

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

2.990 × 10⁹⁹(100-digit number)

29906025357975318642…23609549390895185919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.990 × 10⁹⁹(100-digit number)

29906025357975318642…23609549390895185921

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