Block #96,771

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 9:21:07 AM · Difficulty 9.2792 · 6,694,688 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

748a0c99fdb250923232c9fbe0c5d9dd7c982033221211e71ea7ea5c73ab5e04

View on Chainz ↗

Height

#96,771

Difficulty

9.279248

Transactions

Size

870 B

Version

Bits

09477cce

Nonce

97,206

Timestamp

8/4/2013, 9:21:07 AM

Confirmations

6,694,688

Merkle Root

65e3bc41e7837226dac34ac4ca757814d2732665032dad09c42824876d617635

Transactions (2)

Coinbase4b88433d545120…588c45ec9cfbc0

1 in → 1 out11.6100 XPM109 B

AdqQdWgZ…xXKkKYVY

bf07dfea6ffdb0…f5314c816a1981

4 in → 2 out29.0018 XPM668 B

AczsqSBv…oaUSvwEC AHUbt4Ww…hcxVK8Cp

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.

3.131 × 10¹⁰¹(102-digit number)

31314808814479194651…61626256849089171839

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

3.131 × 10¹⁰¹(102-digit number)

31314808814479194651…61626256849089171839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.131 × 10¹⁰¹(102-digit number)

31314808814479194651…61626256849089171841

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

6.262 × 10¹⁰¹(102-digit number)

62629617628958389303…23252513698178343679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.262 × 10¹⁰¹(102-digit number)

62629617628958389303…23252513698178343681

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

1.252 × 10¹⁰²(103-digit number)

12525923525791677860…46505027396356687359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.252 × 10¹⁰²(103-digit number)

12525923525791677860…46505027396356687361

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

2.505 × 10¹⁰²(103-digit number)

25051847051583355721…93010054792713374719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.505 × 10¹⁰²(103-digit number)

25051847051583355721…93010054792713374721

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

5.010 × 10¹⁰²(103-digit number)

50103694103166711442…86020109585426749439

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