Block #256,971

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 4:38:44 AM · Difficulty 9.9754 · 6,535,693 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07f6053b3483daff5c0480345a0044c046f85605d156df744740327163232d49

View on Chainz ↗

Height

#256,971

Difficulty

9.975375

Transactions

Size

1.29 KB

Version

Bits

09f9b233

Nonce

3,337

Timestamp

11/12/2013, 4:38:44 AM

Confirmations

6,535,693

Merkle Root

ecbad0d7ed6b6b9aac52920de8ae44a5d2f97a4dcd395d3613625f65885ebfad

Transactions (4)

Coinbaseea0bbd0c0ecb9d…d045b57da459ca

1 in → 2 out10.0600 XPM136 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

be7305e5378cd1…c227b1698a6a38

2 in → 2 out86.5549 XPM373 B

AZdmkNt9…Dk8ffFeU AZ14mzgC…fwGseQaw

8c29d7c8f9adf5…9568f24949d27e

1 in → 6 out49.9900 XPM362 B

AGxYGYHa…FRp3G4Gh AP51GjXg…NhL4hYQz ASBVyvFN…6MGD3E4u AVvBfWAv…s7d3svTc AXjk5GEq…VBxcCVj4

6a08c31440feb3…08a51ba80c6a6a

1 in → 6 out42.9800 XPM361 B

AGxYGYHa…FRp3G4Gh AP51GjXg…NhL4hYQz AVvBfWAv…s7d3svTc AXjk5GEq…VBxcCVj4 AdC9Y7xa…h8BzVv6K

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.

3.547 × 10⁹⁵(96-digit number)

35473444587323495106…30648064614444499999

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

3.547 × 10⁹⁵(96-digit number)

35473444587323495106…30648064614444499999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.547 × 10⁹⁵(96-digit number)

35473444587323495106…30648064614444500001

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

7.094 × 10⁹⁵(96-digit number)

70946889174646990212…61296129228888999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.094 × 10⁹⁵(96-digit number)

70946889174646990212…61296129228889000001

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

1.418 × 10⁹⁶(97-digit number)

14189377834929398042…22592258457777999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.418 × 10⁹⁶(97-digit number)

14189377834929398042…22592258457778000001

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

2.837 × 10⁹⁶(97-digit number)

28378755669858796084…45184516915555999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.837 × 10⁹⁶(97-digit number)

28378755669858796084…45184516915556000001

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

5.675 × 10⁹⁶(97-digit number)

56757511339717592169…90369033831111999999

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