Block #96,394

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 4:25:35 AM · Difficulty 9.2671 · 6,697,773 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db237b215104846c2c9872328517cb9a3ec4d930fc1b295c14aced3bf4b1efab

View on Chainz ↗

Height

#96,394

Difficulty

9.267141

Transactions

Size

867 B

Version

Bits

09446357

Nonce

158,240

Timestamp

8/4/2013, 4:25:35 AM

Confirmations

6,697,773

Merkle Root

29093dfd50d0f1fd08b14f8b498804cf00519470959a9e71a98e754ac218c5af

Transactions (2)

Coinbaseadf96f2972a545…5835fb8e47644b

1 in → 1 out11.6400 XPM109 B

AbVRqbHb…mugxc5KL

d766af17f1b6fe…f0b25e8521ec5b

4 in → 2 out277.0101 XPM667 B

ASDVBfFZ…JizKJugo ASqJmG9f…SQgXHdSL

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.

3.481 × 10⁹⁶(97-digit number)

34819001582264354700…10442347719615079399

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

3.481 × 10⁹⁶(97-digit number)

34819001582264354700…10442347719615079399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.481 × 10⁹⁶(97-digit number)

34819001582264354700…10442347719615079401

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

6.963 × 10⁹⁶(97-digit number)

69638003164528709400…20884695439230158799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.963 × 10⁹⁶(97-digit number)

69638003164528709400…20884695439230158801

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

1.392 × 10⁹⁷(98-digit number)

13927600632905741880…41769390878460317599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.392 × 10⁹⁷(98-digit number)

13927600632905741880…41769390878460317601

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

2.785 × 10⁹⁷(98-digit number)

27855201265811483760…83538781756920635199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.785 × 10⁹⁷(98-digit number)

27855201265811483760…83538781756920635201

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

5.571 × 10⁹⁷(98-digit number)

55710402531622967520…67077563513841270399

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