Block #228,749

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 5:25:23 PM · Difficulty 9.9380 · 6,579,558 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

759a8feaca88b734387c92c475a52279dfa3b6cccba6069f3d9e3d9f27203718

View on Chainz ↗

Height

#228,749

Difficulty

9.938041

Transactions

Size

1.31 KB

Version

Bits

09f02374

Nonce

9,950

Timestamp

10/26/2013, 5:25:23 PM

Confirmations

6,579,558

Mined by

⛏️ }RkAFqKfjezAQpHxUWGcDetimH5AUqX9Ace3g

Merkle Root

2c73d2c0da85c666e6c9b8aef0e5d3c40d82a48d9adc15c6bc27078e920f4322

Transactions (1)

Coinbase2c73d2c0da85c6…27078e920f4322

1 in → 35 out10.0900 XPM1.22 KB

AFqKfjez…qX9Ace3g ANo4YY1x…vnsPRDSU AMbCuLHZ…WSoStwkc AWCfnjpk…hb1ovL8F Acs9SHrk…QJSB8SFG

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.

1.806 × 10⁹⁵(96-digit number)

18063283401404117232…97764705709421718749

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

1.806 × 10⁹⁵(96-digit number)

18063283401404117232…97764705709421718749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.806 × 10⁹⁵(96-digit number)

18063283401404117232…97764705709421718751

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

3.612 × 10⁹⁵(96-digit number)

36126566802808234464…95529411418843437499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.612 × 10⁹⁵(96-digit number)

36126566802808234464…95529411418843437501

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

7.225 × 10⁹⁵(96-digit number)

72253133605616468929…91058822837686874999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.225 × 10⁹⁵(96-digit number)

72253133605616468929…91058822837686875001

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

1.445 × 10⁹⁶(97-digit number)

14450626721123293785…82117645675373749999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.445 × 10⁹⁶(97-digit number)

14450626721123293785…82117645675373750001

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

2.890 × 10⁹⁶(97-digit number)

28901253442246587571…64235291350747499999

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 #228,749

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