Block #250,909

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 5:54:17 PM · Difficulty 9.9692 · 6,548,030 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db4c578fdd1a82d931fe5163643400e825fb38b277474fc5c8b9765e03a2466a

View on Chainz ↗

Height

#250,909

Difficulty

9.969169

Transactions

Size

2.14 KB

Version

Bits

09f81b73

Nonce

17,278

Timestamp

11/8/2013, 5:54:17 PM

Confirmations

6,548,030

Mined by

⛏️ aR}%%1ALdHh27brbEqnGMrZaaR18HaaAXNbqrvPf

Merkle Root

ae8751327d30c3ee0876c93423d08b7ec18cee09adbe879efa0c0b08c7f9247b

Transactions (1)

Coinbaseae8751327d30c3…0c0b08c7f9247b

1 in → 60 out10.0200 XPM2.05 KB

ALdHh27b…XNbqrvPf AQtzUSwq…htAuF3yC AUvzrouC…om76UcPR AK5NySZf…XzNDwZSM AKDTDDtx…iqvw9cdY

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.

2.110 × 10⁹²(93-digit number)

21107864821713730477…51551483137729597439

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

2.110 × 10⁹²(93-digit number)

21107864821713730477…51551483137729597439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.110 × 10⁹²(93-digit number)

21107864821713730477…51551483137729597441

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

4.221 × 10⁹²(93-digit number)

42215729643427460954…03102966275459194879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.221 × 10⁹²(93-digit number)

42215729643427460954…03102966275459194881

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

8.443 × 10⁹²(93-digit number)

84431459286854921908…06205932550918389759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.443 × 10⁹²(93-digit number)

84431459286854921908…06205932550918389761

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

1.688 × 10⁹³(94-digit number)

16886291857370984381…12411865101836779519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.688 × 10⁹³(94-digit number)

16886291857370984381…12411865101836779521

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

3.377 × 10⁹³(94-digit number)

33772583714741968763…24823730203673559039

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