Block #517,190

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2014, 7:17:41 PM · Difficulty 10.8507 · 6,285,043 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb4fa59da33df937a02798d7969143140cf80bea3fad41ea6bee133ea4c7f4ab

View on Chainz ↗

Height

#517,190

Difficulty

10.850670

Transactions

Size

1.15 KB

Version

Bits

0ad9c584

Nonce

43,364,361

Timestamp

4/29/2014, 7:17:41 PM

Confirmations

6,285,043

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c0268f6e092ade8352e7efc0dd7f7d898df057cb26160b80feb3efacc4d6c645

Transactions (2)

Coinbase9de95d5530833f…4e50a95a404c37

1 in → 1 out8.4900 XPM116 B

AbwWkWZt…kawDhufa

d5dbdf05ae5be7…633ebf9684d72a

6 in → 2 out250.0000 XPM965 B

AY6zxofy…SaX3wdQn AJx7iMnk…N8RWo8Ci

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.

1.230 × 10¹⁰¹(102-digit number)

12306960619238267909…70678602824288829439

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

1.230 × 10¹⁰¹(102-digit number)

12306960619238267909…70678602824288829439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.230 × 10¹⁰¹(102-digit number)

12306960619238267909…70678602824288829441

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

2.461 × 10¹⁰¹(102-digit number)

24613921238476535819…41357205648577658879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.461 × 10¹⁰¹(102-digit number)

24613921238476535819…41357205648577658881

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

4.922 × 10¹⁰¹(102-digit number)

49227842476953071638…82714411297155317759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.922 × 10¹⁰¹(102-digit number)

49227842476953071638…82714411297155317761

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

9.845 × 10¹⁰¹(102-digit number)

98455684953906143276…65428822594310635519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.845 × 10¹⁰¹(102-digit number)

98455684953906143276…65428822594310635521

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

1.969 × 10¹⁰²(103-digit number)

19691136990781228655…30857645188621271039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.969 × 10¹⁰²(103-digit number)

19691136990781228655…30857645188621271041

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