Block #159,544

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 5:01:36 AM · Difficulty 9.8651 · 6,637,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29741cae0718f9721bc59cdbdbc0a81549e8abe1e7dd5f2ab3777e4a3cf76374

View on Chainz ↗

Height

#159,544

Difficulty

9.865136

Transactions

Size

1.40 KB

Version

Bits

09dd7986

Nonce

116,836

Timestamp

9/11/2013, 5:01:36 AM

Confirmations

6,637,137

Mined by

⛏️ P2SHAKUegfDdkwE8cLmJU3Kgt3YKpswwHBC13P

Merkle Root

011b7b122ac9adbec732dc27b677f5d69fdf6ee08dc63ba4bc081f8e0afd6b94

Transactions (3)

Coinbasef57b00cc162eed…3195ee6adc1a46

1 in → 1 out10.2800 XPM109 B

AKUegfDd…wwHBC13P

3067561049f521…8efb93ad7845a3

4 in → 2 out38.4281 XPM672 B

AXc74VU9…DQbBR4Gs AVpk6176…UGgHkbpp

61b3b91f6b8902…af4fdb2fc1f9db

4 in → 1 out21.0000 XPM567 B

AFz9fXym…wh4UqpkL

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.

1.260 × 10⁹⁵(96-digit number)

12606144012198116837…10429757349360683319

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

1.260 × 10⁹⁵(96-digit number)

12606144012198116837…10429757349360683319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.260 × 10⁹⁵(96-digit number)

12606144012198116837…10429757349360683321

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

2.521 × 10⁹⁵(96-digit number)

25212288024396233674…20859514698721366639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.521 × 10⁹⁵(96-digit number)

25212288024396233674…20859514698721366641

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

5.042 × 10⁹⁵(96-digit number)

50424576048792467348…41719029397442733279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.042 × 10⁹⁵(96-digit number)

50424576048792467348…41719029397442733281

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

1.008 × 10⁹⁶(97-digit number)

10084915209758493469…83438058794885466559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.008 × 10⁹⁶(97-digit number)

10084915209758493469…83438058794885466561

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

2.016 × 10⁹⁶(97-digit number)

20169830419516986939…66876117589770933119

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