Block #904,258

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2015, 6:52:10 PM · Difficulty 10.9373 · 5,905,554 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4e995c6ad7cc2132a9a3466e2e45fdc0e6fa7ee98de37b0ff63aa6cdf00d8b0

View on Chainz ↗

Height

#904,258

Difficulty

10.937327

Transactions

Size

594 B

Version

Bits

0aeff4af

Nonce

12,549

Timestamp

1/21/2015, 6:52:10 PM

Confirmations

5,905,554

Mined by

⛏️ BAXz2kWvXMhDXBmF1MPgL7ZtTCLV5ZFCDBd

Merkle Root

1f392ef8f2ff96e20e912ae61d9149d98d8bc998de1e47b86e4892624c9cfd9e

Transactions (1)

Coinbase1f392ef8f2ff96…4892624c9cfd9e

1 in → 13 out8.3500 XPM505 B

AXz2kWvX…V5ZFCDBd AJzWx2VD…j4ZSMit5 AHH8JjCP…zqhsmuVM AGz9gyZW…bo8NYQpw AKF9hNmX…pjjmh9Dc

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.

2.346 × 10⁹²(93-digit number)

23466696895412595805…13594048595132567039

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

2.346 × 10⁹²(93-digit number)

23466696895412595805…13594048595132567039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.346 × 10⁹²(93-digit number)

23466696895412595805…13594048595132567041

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

4.693 × 10⁹²(93-digit number)

46933393790825191610…27188097190265134079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.693 × 10⁹²(93-digit number)

46933393790825191610…27188097190265134081

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

9.386 × 10⁹²(93-digit number)

93866787581650383220…54376194380530268159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.386 × 10⁹²(93-digit number)

93866787581650383220…54376194380530268161

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

1.877 × 10⁹³(94-digit number)

18773357516330076644…08752388761060536319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.877 × 10⁹³(94-digit number)

18773357516330076644…08752388761060536321

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

3.754 × 10⁹³(94-digit number)

37546715032660153288…17504777522121072639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.754 × 10⁹³(94-digit number)

37546715032660153288…17504777522121072641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #904,258

Cookie Preferences