Block #221,862

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 7:52:31 PM · Difficulty 9.9398 · 6,576,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49e7de3abaeb47772fa164889cc6bdc8402319093a47ddf9d70c5878a8aa23f1

View on Chainz ↗

Height

#221,862

Difficulty

9.939780

Transactions

Size

5.78 KB

Version

Bits

09f09564

Nonce

53,544

Timestamp

10/21/2013, 7:52:31 PM

Confirmations

6,576,052

Mined by

⛏️ P2SHAUi25ouRfRRV4we4c4BPgvHREfqajyFuZV

Merkle Root

71f31108a0dfff17da71b9ead5a68b3c89c29205435a60c3b4692844fc15cf1c

Transactions (5)

Coinbasef902c5f62904ef…ba1275119e05b9

1 in → 1 out10.1900 XPM109 B

AUi25ouR…qajyFuZV

d740f71ffa33b6…573fdd52b95b8e

1 in → 1 out10.1500 XPM157 B

AKagxX7i…AQPtvdhU

47917abfd04aad…b028f9d686f65d

3 in → 4 out12.4662 XPM555 B

AVtQKuHZ…XqZkeLEZ AHRnoPQw…SLFKBYxM AHLyZUb7…cHnQjZJ9 AbuU1HhS…JPwsJEbB

00afb04546a755…4b6f206a1acf42

32 in → 1 out10.0087 XPM4.67 KB

APfnkyGJ…rue7ZTJD

9742a625a73928…a00844ae2ed3e6

1 in → 2 out3.7336 XPM226 B

ATtkfa6o…2cnR55io AKnkWB4Q…C9MjNcj3

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.

1.162 × 10⁹⁸(99-digit number)

11625352728914816362…49446535312392320639

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

1.162 × 10⁹⁸(99-digit number)

11625352728914816362…49446535312392320639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.162 × 10⁹⁸(99-digit number)

11625352728914816362…49446535312392320641

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

2.325 × 10⁹⁸(99-digit number)

23250705457829632725…98893070624784641279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.325 × 10⁹⁸(99-digit number)

23250705457829632725…98893070624784641281

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

4.650 × 10⁹⁸(99-digit number)

46501410915659265451…97786141249569282559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.650 × 10⁹⁸(99-digit number)

46501410915659265451…97786141249569282561

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

9.300 × 10⁹⁸(99-digit number)

93002821831318530902…95572282499138565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.300 × 10⁹⁸(99-digit number)

93002821831318530902…95572282499138565121

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

1.860 × 10⁹⁹(100-digit number)

18600564366263706180…91144564998277130239

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