Block #278,140

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 8:53:16 PM · Difficulty 9.9682 · 6,516,910 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0f81fe518092f1eae056a6cdb213f301c1e8599e3177650f0af38b661f64564

View on Chainz ↗

Height

#278,140

Difficulty

9.968150

Transactions

Size

1.08 KB

Version

Bits

09f7d8b2

Nonce

72,383

Timestamp

11/27/2013, 8:53:16 PM

Confirmations

6,516,910

Mined by

⛏️ |>aRAN8nUzffzPFGV1c5CDiMhELQSRYcDfRDQ2

Merkle Root

5d30605e094496d8a0724a0f5d7f884463ebb325a51ad5e1df8d398e31c06784

Transactions (1)

Coinbase5d30605e094496…8d398e31c06784

1 in → 28 out10.0300 XPM1015 B

AN8nUzff…YcDfRDQ2 AbiApRgN…g8QuFUwL AJ9QW1VP…GmAJhvhc AaRQgKTk…f5H51M47 AeKQQ68U…WbyBWyts

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.

5.521 × 10⁹³(94-digit number)

55218054447618877790…56675041058327031039

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

5.521 × 10⁹³(94-digit number)

55218054447618877790…56675041058327031039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.521 × 10⁹³(94-digit number)

55218054447618877790…56675041058327031041

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

1.104 × 10⁹⁴(95-digit number)

11043610889523775558…13350082116654062079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.104 × 10⁹⁴(95-digit number)

11043610889523775558…13350082116654062081

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

2.208 × 10⁹⁴(95-digit number)

22087221779047551116…26700164233308124159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.208 × 10⁹⁴(95-digit number)

22087221779047551116…26700164233308124161

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

4.417 × 10⁹⁴(95-digit number)

44174443558095102232…53400328466616248319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.417 × 10⁹⁴(95-digit number)

44174443558095102232…53400328466616248321

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

8.834 × 10⁹⁴(95-digit number)

88348887116190204465…06800656933232496639

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