Block #209,766

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 6:07:04 PM · Difficulty 9.9112 · 6,585,288 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c5ab9376bff192bd3742a4c5190a0eca356526aadc4a6e798088fc3f21787dd

View on Chainz ↗

Height

#209,766

Difficulty

9.911179

Transactions

Size

1.21 KB

Version

Bits

09e94302

Nonce

19,292

Timestamp

10/14/2013, 6:07:04 PM

Confirmations

6,585,288

Mined by

⛏️ P2SHAZz6Bg87J8VhAYyRKDwNgf7vf5MZtiQn8U

Merkle Root

168d02d97c4e29a0792d17a9d0ebbf210b4a1d5392931b1388cd336c32a4bb08

Transactions (2)

Coinbasee8582fffd15c72…ee0456f8227e57

1 in → 1 out10.1800 XPM109 B

AZz6Bg87…MZtiQn8U

5c9b4c2158df1b…ce240ad37efcdf

7 in → 1 out23.6939 XPM1.02 KB

AKujDzwc…hB47iK1m

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.

6.019 × 10⁹⁰(91-digit number)

60198697417708985146…78716762270167619079

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

6.019 × 10⁹⁰(91-digit number)

60198697417708985146…78716762270167619079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.019 × 10⁹⁰(91-digit number)

60198697417708985146…78716762270167619081

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

1.203 × 10⁹¹(92-digit number)

12039739483541797029…57433524540335238159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.203 × 10⁹¹(92-digit number)

12039739483541797029…57433524540335238161

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

2.407 × 10⁹¹(92-digit number)

24079478967083594058…14867049080670476319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.407 × 10⁹¹(92-digit number)

24079478967083594058…14867049080670476321

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

4.815 × 10⁹¹(92-digit number)

48158957934167188116…29734098161340952639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.815 × 10⁹¹(92-digit number)

48158957934167188116…29734098161340952641

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

9.631 × 10⁹¹(92-digit number)

96317915868334376233…59468196322681905279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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