Block #275,072

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 1:27:36 PM · Difficulty 9.9596 · 6,519,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b77630ac1009a0ff0e6887a295305e416a5ebd7ff54c64c2ce2f7b3e69ba641e

View on Chainz ↗

Height

#275,072

Difficulty

9.959611

Transactions

Size

3.75 KB

Version

Bits

09f5a911

Nonce

39,125

Timestamp

11/26/2013, 1:27:36 PM

Confirmations

6,519,884

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f92a4b3a57ddd2753928ac63095a95aeb4c9e6d4cc0fd4b67d91f59fc129174e

Transactions (5)

Coinbase4ead88d35e5757…583a78842adbd5

1 in → 1 out10.1400 XPM110 B

AeKNrjNj…1NEq95Ta

5f4ecea97d6925…38b731a6e776aa

12 in → 2 out222.2694 XPM1.81 KB

AG9ATjVa…xAfv8yay AUPNwzcD…Ta9eW631

939df97fc0fba6…1398e8b8f7128e

7 in → 2 out200.0000 XPM1.09 KB

AQvftpUz…fw8JQAtz AT278vm4…3NwHX1M3

b2faeac20c7081…8971bd59f39ac1

2 in → 1 out20.1500 XPM271 B

AYuv4nFV…T1ofBzD9

2d21ea008699b7…f744b8defd0d76

2 in → 5 out20.1700 XPM408 B

AGvfuVzL…tTBUySRN ASsZ8gkf…EvjaZhvT AeKNrjNj…1NEq95Ta AFx4pUv4…deee42SL AU6bVD2o…JjzwJGx9

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.

8.611 × 10⁹¹(92-digit number)

86112582411254458665…99261177390804839039

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

8.611 × 10⁹¹(92-digit number)

86112582411254458665…99261177390804839039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.611 × 10⁹¹(92-digit number)

86112582411254458665…99261177390804839041

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

1.722 × 10⁹²(93-digit number)

17222516482250891733…98522354781609678079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.722 × 10⁹²(93-digit number)

17222516482250891733…98522354781609678081

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

3.444 × 10⁹²(93-digit number)

34445032964501783466…97044709563219356159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.444 × 10⁹²(93-digit number)

34445032964501783466…97044709563219356161

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

6.889 × 10⁹²(93-digit number)

68890065929003566932…94089419126438712319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.889 × 10⁹²(93-digit number)

68890065929003566932…94089419126438712321

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

1.377 × 10⁹³(94-digit number)

13778013185800713386…88178838252877424639

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