Block #236,413

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 11:51:15 AM · Difficulty 9.9474 · 6,559,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1dca85d9ef8a54d658a04683550e01cbdea9b10b4912a565634f30d75b95309b

View on Chainz ↗

Height

#236,413

Difficulty

9.947432

Transactions

Size

1.94 KB

Version

Bits

09f28ae4

Nonce

21,969

Timestamp

10/31/2013, 11:51:15 AM

Confirmations

6,559,667

Mined by

⛏️ }RrD@ARanXFdqZu3gw2gscjananFaiq2FNquU2w

Merkle Root

338ea0c4f0b4828c6f986f75697d0db27285ad4477df2aec3bd7d95a9b851c1c

Transactions (1)

Coinbase338ea0c4f0b482…d7d95a9b851c1c

1 in → 54 out10.0700 XPM1.85 KB

ARanXFdq…2FNquU2w AL8BLb6A…ZXGDBoCK ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

3.844 × 10⁹⁴(95-digit number)

38444199848070562232…02239132620284799999

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

3.844 × 10⁹⁴(95-digit number)

38444199848070562232…02239132620284799999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.844 × 10⁹⁴(95-digit number)

38444199848070562232…02239132620284800001

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

7.688 × 10⁹⁴(95-digit number)

76888399696141124464…04478265240569599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.688 × 10⁹⁴(95-digit number)

76888399696141124464…04478265240569600001

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

1.537 × 10⁹⁵(96-digit number)

15377679939228224892…08956530481139199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.537 × 10⁹⁵(96-digit number)

15377679939228224892…08956530481139200001

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

3.075 × 10⁹⁵(96-digit number)

30755359878456449785…17913060962278399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.075 × 10⁹⁵(96-digit number)

30755359878456449785…17913060962278400001

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

6.151 × 10⁹⁵(96-digit number)

61510719756912899571…35826121924556799999

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