Block #215,932

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 10:46:39 AM · Difficulty 9.9252 · 6,595,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be9fdd8b39685c92b1693256efa7ae23ab9b2247bc6709ca22f72bd1b5ec60b7

View on Chainz ↗

Height

#215,932

Difficulty

9.925241

Transactions

Size

1.94 KB

Version

Bits

09ecdc9e

Nonce

8,742

Timestamp

10/18/2013, 10:46:39 AM

Confirmations

6,595,128

Mined by

⛏️ |KRaAdxeWJwMdhQmzp8UXQGk2g11qEXPALzofH

Merkle Root

d7bc825a8fde934dfbc57b59e52ab163e2ff0e508053dc2ab97ff9e29aefb7fe

Transactions (1)

Coinbased7bc825a8fde93…7ff9e29aefb7fe

1 in → 54 out10.1200 XPM1.85 KB

AdxeWJwM…XPALzofH AabHNb1B…GRoingRy AKXeSXzu…yeuNjvhB ANmkKL2U…jPxj1Qs3 Aaox8Rxx…XTyyJXVx

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.

3.034 × 10⁹⁰(91-digit number)

30347844373107264767…35408985616647315839

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

3.034 × 10⁹⁰(91-digit number)

30347844373107264767…35408985616647315839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.034 × 10⁹⁰(91-digit number)

30347844373107264767…35408985616647315841

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

6.069 × 10⁹⁰(91-digit number)

60695688746214529534…70817971233294631679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.069 × 10⁹⁰(91-digit number)

60695688746214529534…70817971233294631681

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

1.213 × 10⁹¹(92-digit number)

12139137749242905906…41635942466589263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.213 × 10⁹¹(92-digit number)

12139137749242905906…41635942466589263361

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

2.427 × 10⁹¹(92-digit number)

24278275498485811813…83271884933178526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.427 × 10⁹¹(92-digit number)

24278275498485811813…83271884933178526721

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

4.855 × 10⁹¹(92-digit number)

48556550996971623627…66543769866357053439

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 #215,932

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