Block #519,244

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2014, 3:03:46 AM · Difficulty 10.8550 · 6,287,068 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3bf0eaa8b03484db7e20aee6b43883a7095cd076a82104240ee30883232a58ba

View on Chainz ↗

Height

#519,244

Difficulty

10.855019

Transactions

Size

609 B

Version

Bits

0adae27f

Nonce

4,331

Timestamp

5/1/2014, 3:03:46 AM

Confirmations

6,287,068

Mined by

⛏️ P2SHAV9GM9Aq6LFBae5EXKFEBHneNBanGnxvkD

Merkle Root

ebe39ac01dc2f940261909271e3d6fbb1ec9a68b8fe2d71ad1a9b27994f9cf2a

Transactions (2)

Coinbase9ca306baa73e0c…e5a5cfaab1e246

1 in → 1 out8.4800 XPM110 B

AV9GM9Aq…anGnxvkD

03655b28739343…2168d9655302cc

2 in → 4 out9.4604 XPM408 B

AeKNrjNj…1NEq95Ta ARJQsNEx…UvYvuSPW Abo6THXy…XGrxXxo7 AcBvLaSu…X3gaHvJ1

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.

1.226 × 10⁹⁶(97-digit number)

12263369890873538110…28679252738984477479

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

1.226 × 10⁹⁶(97-digit number)

12263369890873538110…28679252738984477479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.226 × 10⁹⁶(97-digit number)

12263369890873538110…28679252738984477481

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

2.452 × 10⁹⁶(97-digit number)

24526739781747076221…57358505477968954959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.452 × 10⁹⁶(97-digit number)

24526739781747076221…57358505477968954961

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

4.905 × 10⁹⁶(97-digit number)

49053479563494152443…14717010955937909919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.905 × 10⁹⁶(97-digit number)

49053479563494152443…14717010955937909921

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

9.810 × 10⁹⁶(97-digit number)

98106959126988304887…29434021911875819839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.810 × 10⁹⁶(97-digit number)

98106959126988304887…29434021911875819841

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

1.962 × 10⁹⁷(98-digit number)

19621391825397660977…58868043823751639679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.962 × 10⁹⁷(98-digit number)

19621391825397660977…58868043823751639681

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 #519,244

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