Block #267,332

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 4:55:29 AM · Difficulty 9.9591 · 6,531,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3e6dad65684062e9f5fe5ef32baac72f8a86e6ef88b1d68b66ed955d6ffffce

View on Chainz ↗

Height

#267,332

Difficulty

9.959128

Transactions

Size

1.40 KB

Version

Bits

09f58969

Nonce

25,814

Timestamp

11/21/2013, 4:55:29 AM

Confirmations

6,531,983

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

83e17e22b15c38cdc938f1231676661642a7dd352458d9b2cc1edc5d27007a2e

Transactions (3)

Coinbase168db81ddfa69d…9a10c796ab57d7

1 in → 2 out10.0900 XPM141 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

f9db0d35c0b801…24e6715e84db59

3 in → 2 out65.2362 XPM523 B

AeQXgyJb…2HS9aFew AM4DUx4F…6EcjKqgF

6e711caee37d16…36728e5dda7f84

4 in → 2 out74.9713 XPM672 B

AHoYPz5v…gUYhavNq AHG1qvHK…qetzqL9b

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.

7.453 × 10¹⁰⁰(101-digit number)

74533106759625843580…69194651642724746879

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

7.453 × 10¹⁰⁰(101-digit number)

74533106759625843580…69194651642724746879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.453 × 10¹⁰⁰(101-digit number)

74533106759625843580…69194651642724746881

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

1.490 × 10¹⁰¹(102-digit number)

14906621351925168716…38389303285449493759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.490 × 10¹⁰¹(102-digit number)

14906621351925168716…38389303285449493761

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

2.981 × 10¹⁰¹(102-digit number)

29813242703850337432…76778606570898987519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.981 × 10¹⁰¹(102-digit number)

29813242703850337432…76778606570898987521

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

5.962 × 10¹⁰¹(102-digit number)

59626485407700674864…53557213141797975039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.962 × 10¹⁰¹(102-digit number)

59626485407700674864…53557213141797975041

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

1.192 × 10¹⁰²(103-digit number)

11925297081540134972…07114426283595950079

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