Block #245,399

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 10:52:13 AM · Difficulty 9.9639 · 6,546,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3dbd912c5990bb7b4d2efc99e718df8a9cb9f8f6cd1707801d661e410a7538cf

View on Chainz ↗

Height

#245,399

Difficulty

9.963877

Transactions

Size

2.98 KB

Version

Bits

09f6c09e

Nonce

32,609

Timestamp

11/5/2013, 10:52:13 AM

Confirmations

6,546,488

Merkle Root

cff52bfbb7d66244c92f98c2003513241f2dc0e7ffc73d67c565e0c7b56860af

Transactions (5)

Coinbaseb46c9f0799cf72…7883d3e90c1e1a

1 in → 2 out10.1100 XPM137 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

bc1efd32b25ea1…492993d5f0bf86

11 in → 2 out105.6135 XPM1.66 KB

ALszT3LV…hZKdJfo5 ANP3mT5K…dkjrtVpK

6e683dc837b718…c9821b83a28ce2

3 in → 2 out30.2000 XPM522 B

AN7ZnJS4…uHpiPac9 Ab9AgZ7J…q6U1TZpe

8d07b8029cb620…a5e0488f3f2439

2 in → 2 out18.0740 XPM373 B

ASuoUi24…FwBoFbxd AKAXKPEd…5U9LC5Ei

8d34361b8b06cd…bad33a7cdc0718

1 in → 2 out4.1661 XPM227 B

AZjwrNmt…ZEJK4GGm AMJDChGB…VXxUjXFK

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.

1.134 × 10⁹⁸(99-digit number)

11345948167053572145…38800155461320056799

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

1.134 × 10⁹⁸(99-digit number)

11345948167053572145…38800155461320056799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.134 × 10⁹⁸(99-digit number)

11345948167053572145…38800155461320056801

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

2.269 × 10⁹⁸(99-digit number)

22691896334107144290…77600310922640113599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.269 × 10⁹⁸(99-digit number)

22691896334107144290…77600310922640113601

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

4.538 × 10⁹⁸(99-digit number)

45383792668214288580…55200621845280227199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.538 × 10⁹⁸(99-digit number)

45383792668214288580…55200621845280227201

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

9.076 × 10⁹⁸(99-digit number)

90767585336428577160…10401243690560454399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.076 × 10⁹⁸(99-digit number)

90767585336428577160…10401243690560454401

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

1.815 × 10⁹⁹(100-digit number)

18153517067285715432…20802487381120908799

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