Block #201,366

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 2:38:13 PM · Difficulty 9.8914 · 6,607,223 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6de5d1a434a39934b5ee6c22493025273db70c1f4db978991b4e63e0f0025685

View on Chainz ↗

Height

#201,366

Difficulty

9.891361

Transactions

Size

3.70 KB

Version

Bits

09e43039

Nonce

1,164,796,417

Timestamp

10/9/2013, 2:38:13 PM

Confirmations

6,607,223

Mined by

⛏️ RUiAPHngwz27GMW45jJC6wSAHExgSoXWG6CFr

Merkle Root

73bd0715b845d618d568b4432a8b8f5b138c3ee5723942fb98a19079f6349bb4

Transactions (1)

Coinbase73bd0715b845d6…a19079f6349bb4

1 in → 107 out10.1700 XPM3.61 KB

APHngwz2…oXWG6CFr AHqZtsfn…WrCGjM3J ATeGzPEb…fEYhKxfs AVbJcrD2…qcWAWUdn AbGUqMnw…abP9ZPcY

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.

1.582 × 10⁹³(94-digit number)

15825110161148297303…40419110730227706069

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

1.582 × 10⁹³(94-digit number)

15825110161148297303…40419110730227706069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.582 × 10⁹³(94-digit number)

15825110161148297303…40419110730227706071

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

3.165 × 10⁹³(94-digit number)

31650220322296594606…80838221460455412139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.165 × 10⁹³(94-digit number)

31650220322296594606…80838221460455412141

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

6.330 × 10⁹³(94-digit number)

63300440644593189212…61676442920910824279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.330 × 10⁹³(94-digit number)

63300440644593189212…61676442920910824281

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

1.266 × 10⁹⁴(95-digit number)

12660088128918637842…23352885841821648559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.266 × 10⁹⁴(95-digit number)

12660088128918637842…23352885841821648561

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

2.532 × 10⁹⁴(95-digit number)

25320176257837275684…46705771683643297119

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 #201,366

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