Block #216,742

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 10:00:32 PM · Difficulty 9.9273 · 6,610,340 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9d92267b453cfbf3772fd337eee7e1d4afa5404279c338d65e75d9c00e3ae54

View on Chainz ↗

Height

#216,742

Difficulty

9.927283

Transactions

Size

1.51 KB

Version

Bits

09ed6273

Nonce

125,159

Timestamp

10/18/2013, 10:00:32 PM

Confirmations

6,610,340

Mined by

⛏️ NRamAdL4ZZDRpVXrdizsRm6Y8VcTzG2eQtg1T9

Merkle Root

fda5cbc6351b73deb43a1cf57f2350d096eaa93463fc9d34c6bc9b3e1a8aec7b

Transactions (1)

Coinbasefda5cbc6351b73…bc9b3e1a8aec7b

1 in → 41 out10.1100 XPM1.42 KB

AdL4ZZDR…2eQtg1T9 AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AKFBsJ1Y…LYyU7TbU AHkgKuuD…TkWqWiw1

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.

5.258 × 10⁹³(94-digit number)

52585916929919424372…76291711520974484359

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

5.258 × 10⁹³(94-digit number)

52585916929919424372…76291711520974484359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.258 × 10⁹³(94-digit number)

52585916929919424372…76291711520974484361

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

1.051 × 10⁹⁴(95-digit number)

10517183385983884874…52583423041948968719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.051 × 10⁹⁴(95-digit number)

10517183385983884874…52583423041948968721

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

2.103 × 10⁹⁴(95-digit number)

21034366771967769748…05166846083897937439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.103 × 10⁹⁴(95-digit number)

21034366771967769748…05166846083897937441

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

4.206 × 10⁹⁴(95-digit number)

42068733543935539497…10333692167795874879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.206 × 10⁹⁴(95-digit number)

42068733543935539497…10333692167795874881

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

8.413 × 10⁹⁴(95-digit number)

84137467087871078995…20667384335591749759

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

Block #216,742

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