Block #248,704

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 1:05:43 PM · Difficulty 9.9660 · 6,566,327 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9367b2e9548b314342b9a9006618b97ce12d8ca127dc834cfc9e669a115bd609

View on Chainz ↗

Height

#248,704

Difficulty

9.966035

Transactions

Size

1.94 KB

Version

Bits

09f74e0c

Nonce

7,212

Timestamp

11/7/2013, 1:05:43 PM

Confirmations

6,566,327

Mined by

⛏️ R{APvpz12Ne3y3GdSQX5xb8QzBwoNjdsxTYA

Merkle Root

7387950de9ad765a556e91ecb1ce7764feaa82356cd70b1e34b4c5022e6bc555

Transactions (1)

Coinbase7387950de9ad76…b4c5022e6bc555

1 in → 54 out10.0300 XPM1.85 KB

APvpz12N…NjdsxTYA ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU

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.

3.040 × 10¹⁰⁰(101-digit number)

30402473446477297846…80515483345392972799

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

3.040 × 10¹⁰⁰(101-digit number)

30402473446477297846…80515483345392972799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.040 × 10¹⁰⁰(101-digit number)

30402473446477297846…80515483345392972801

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

6.080 × 10¹⁰⁰(101-digit number)

60804946892954595693…61030966690785945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.080 × 10¹⁰⁰(101-digit number)

60804946892954595693…61030966690785945601

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

1.216 × 10¹⁰¹(102-digit number)

12160989378590919138…22061933381571891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.216 × 10¹⁰¹(102-digit number)

12160989378590919138…22061933381571891201

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

2.432 × 10¹⁰¹(102-digit number)

24321978757181838277…44123866763143782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.432 × 10¹⁰¹(102-digit number)

24321978757181838277…44123866763143782401

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

4.864 × 10¹⁰¹(102-digit number)

48643957514363676554…88247733526287564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.864 × 10¹⁰¹(102-digit number)

48643957514363676554…88247733526287564801

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 #248,704

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