Block #312,300

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 12/14/2013, 11:04:21 PM · Difficulty 9.9958 · 6,490,189 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

10ed6ca3c058b0dcb6e1f92768995dab8aea7a820ef8b823d5a50523d07609ce

View on Chainz ↗

Height

#312,300

Difficulty

9.995772

Transactions

Size

1.08 KB

Version

Bits

09feeaf1

Nonce

53,784

Timestamp

12/14/2013, 11:04:21 PM

Confirmations

6,490,189

Mined by

⛏️ P2SHAWT4FajAqvKnh9YhmpgjgT5GAa7qUxCsaJ

Merkle Root

788bc577f8ee1e5a0bd8d7d3acf99270485fec6efd39a35ceff91788f262f9c2

Transactions (5)

Coinbase7d89ffffda321f…87fc7d36912e25

1 in → 1 out10.0300 XPM109 B

AWT4FajA…7qUxCsaJ

eba6464fe09a35…c623e6f226de1a

1 in → 2 out5.3566 XPM225 B

AcxTSowA…x3MyDmeA AWHqSsod…S114Gc1Y

6601565345db92…63b450bce21345

1 in → 2 out4.8194 XPM227 B

Aegpabhz…DrseJPwq ALMirCbi…KRkkad2x

ee5800daafb262…103f16c666c6ad

1 in → 2 out3.4332 XPM227 B

AVCXQFU9…ndSyK98w AYW62HqN…FYoAS6pU

63c4f2060b4cda…c12a36a9e9bfb2

1 in → 2 out2.5041 XPM227 B

AHCPJrY3…RrLhmCmp AQtfdk1i…ZcpYzmGg

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.

1.855 × 10⁹⁷(98-digit number)

18557636464203621893…54987069712789393919

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

1.855 × 10⁹⁷(98-digit number)

18557636464203621893…54987069712789393919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.855 × 10⁹⁷(98-digit number)

18557636464203621893…54987069712789393921

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

3.711 × 10⁹⁷(98-digit number)

37115272928407243787…09974139425578787839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.711 × 10⁹⁷(98-digit number)

37115272928407243787…09974139425578787841

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

7.423 × 10⁹⁷(98-digit number)

74230545856814487575…19948278851157575679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.423 × 10⁹⁷(98-digit number)

74230545856814487575…19948278851157575681

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

1.484 × 10⁹⁸(99-digit number)

14846109171362897515…39896557702315151359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.484 × 10⁹⁸(99-digit number)

14846109171362897515…39896557702315151361

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

2.969 × 10⁹⁸(99-digit number)

29692218342725795030…79793115404630302719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.969 × 10⁹⁸(99-digit number)

29692218342725795030…79793115404630302721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.938 × 10⁹⁸(99-digit number)

59384436685451590060…59586230809260605439

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

5.938 × 10⁹⁸(99-digit number)

59384436685451590060…59586230809260605441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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