Block #102,267

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 1:55:50 AM · Difficulty 9.4880 · 6,715,009 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41fca8766135b45160ac9752b2c2b7852dfe0a12133c83421bfc1d48e16d5b97

View on Chainz ↗

Height

#102,267

Difficulty

9.487961

Transactions

Size

3.02 KB

Version

Bits

097ceb0b

Nonce

17,744

Timestamp

8/7/2013, 1:55:50 AM

Confirmations

6,715,009

Mined by

⛏️ P2SHAWjf2z2jWfbneQHtvrEdDduLucgKtZA2Ws

Merkle Root

835420b1a100a69ecd1c909b80ef070a589c7bee17a655e713bafb829347352b

Transactions (2)

Coinbaseaacfe8b0fc169b…b671f4cd0758b8

1 in → 1 out11.1200 XPM109 B

AWjf2z2j…gKtZA2Ws

7a8b3c31ec5427…260686add920ff

25 in → 1 out312.0000 XPM2.82 KB

AMojYk3E…DzzgBLgu

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.

7.807 × 10¹⁰⁶(107-digit number)

78077985759886724576…15895547122525438319

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

7.807 × 10¹⁰⁶(107-digit number)

78077985759886724576…15895547122525438319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.807 × 10¹⁰⁶(107-digit number)

78077985759886724576…15895547122525438321

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

1.561 × 10¹⁰⁷(108-digit number)

15615597151977344915…31791094245050876639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.561 × 10¹⁰⁷(108-digit number)

15615597151977344915…31791094245050876641

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

3.123 × 10¹⁰⁷(108-digit number)

31231194303954689830…63582188490101753279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.123 × 10¹⁰⁷(108-digit number)

31231194303954689830…63582188490101753281

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

6.246 × 10¹⁰⁷(108-digit number)

62462388607909379661…27164376980203506559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.246 × 10¹⁰⁷(108-digit number)

62462388607909379661…27164376980203506561

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

1.249 × 10¹⁰⁸(109-digit number)

12492477721581875932…54328753960407013119

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 #102,267

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