Block #175,426

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 7:17:07 AM · Difficulty 9.8635 · 6,620,687 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b7f7c2ec436419c4df46d187f51897370b0bec48f40733b8e1583b959ab115b

View on Chainz ↗

Height

#175,426

Difficulty

9.863512

Transactions

Size

357 B

Version

Bits

09dd0f22

Nonce

20,813

Timestamp

9/22/2013, 7:17:07 AM

Confirmations

6,620,687

Mined by

⛏️ P2SHARPU9skP7dKWz4Ka74pUfeVsjQDoRVGg3C

Merkle Root

23021773f6e318825f55bfe28c3794f81b3bbf9760bffa230a1837fb370133f2

Transactions (2)

Coinbasee71d161e702b14…b021a8971c2721

1 in → 1 out10.2700 XPM109 B

ARPU9skP…DoRVGg3C

b412b5e73550a3…34d47cdb02b0b9

1 in → 1 out10.2500 XPM157 B

ALuoRFYG…mxTQxQct

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.

4.644 × 10⁹⁶(97-digit number)

46447155500704798805…56459286922611528429

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

4.644 × 10⁹⁶(97-digit number)

46447155500704798805…56459286922611528429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.644 × 10⁹⁶(97-digit number)

46447155500704798805…56459286922611528431

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

9.289 × 10⁹⁶(97-digit number)

92894311001409597610…12918573845223056859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.289 × 10⁹⁶(97-digit number)

92894311001409597610…12918573845223056861

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

1.857 × 10⁹⁷(98-digit number)

18578862200281919522…25837147690446113719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.857 × 10⁹⁷(98-digit number)

18578862200281919522…25837147690446113721

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

3.715 × 10⁹⁷(98-digit number)

37157724400563839044…51674295380892227439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.715 × 10⁹⁷(98-digit number)

37157724400563839044…51674295380892227441

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

7.431 × 10⁹⁷(98-digit number)

74315448801127678088…03348590761784454879

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