Block #296,032

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 6:43:12 PM · Difficulty 9.9916 · 6,520,867 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d36e8521d4ee6ef1e6961678042b67654549e1864ce732a8081004d199b6224

View on Chainz ↗

Height

#296,032

Difficulty

9.991602

Transactions

Size

1.08 KB

Version

Bits

09fdd99a

Nonce

37,561

Timestamp

12/5/2013, 6:43:12 PM

Confirmations

6,520,867

Mined by

⛏️ `aRUAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

dadda5fc457815b842fef5b7271139a4b761cfbb178cffbbe4b80e9b29e58469

Transactions (1)

Coinbasedadda5fc457815…b80e9b29e58469

1 in → 28 out9.9800 XPM1015 B

AQwRN8bE…V8PsTcY9 AKEwr54i…9BfmMkRh AYtDvcGs…VuAcA7m7 AWA5FEzr…x9RdPKTy AVzfxgRz…xjF9JZFi

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.

2.461 × 10⁹⁹(100-digit number)

24610859697135746318…20411237134163725599

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

2.461 × 10⁹⁹(100-digit number)

24610859697135746318…20411237134163725599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.461 × 10⁹⁹(100-digit number)

24610859697135746318…20411237134163725601

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

4.922 × 10⁹⁹(100-digit number)

49221719394271492636…40822474268327451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.922 × 10⁹⁹(100-digit number)

49221719394271492636…40822474268327451201

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

9.844 × 10⁹⁹(100-digit number)

98443438788542985273…81644948536654902399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.844 × 10⁹⁹(100-digit number)

98443438788542985273…81644948536654902401

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

1.968 × 10¹⁰⁰(101-digit number)

19688687757708597054…63289897073309804799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.968 × 10¹⁰⁰(101-digit number)

19688687757708597054…63289897073309804801

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

3.937 × 10¹⁰⁰(101-digit number)

39377375515417194109…26579794146619609599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.937 × 10¹⁰⁰(101-digit number)

39377375515417194109…26579794146619609601

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 #296,032

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