Block #356,225

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 3:16:32 PM · Difficulty 10.3737 · 6,456,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

921bc10c7d6db3295e81445c27e8715db1a75df36d8bc0a0daa837cdf2aa2f5c

View on Chainz ↗

Height

#356,225

Difficulty

10.373677

Transactions

Size

429 B

Version

Bits

0a5fa950

Nonce

201,888

Timestamp

1/12/2014, 3:16:32 PM

Confirmations

6,456,758

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c79529a332bc7f78072f23e30505ad98e37e7905313096aab9af46a90ae84663

Transactions (2)

Coinbase654d6d90f8bd4e…46f9d385ed9bb5

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

70a956a503caee…534a6f8b1d0489

1 in → 2 out12901.1573 XPM226 B

AMpTFoaa…bppLAZFs AKmMW5gh…cFAehmat

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.

1.921 × 10¹⁰²(103-digit number)

19217809918887574082…88904885321496349599

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

1.921 × 10¹⁰²(103-digit number)

19217809918887574082…88904885321496349599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.921 × 10¹⁰²(103-digit number)

19217809918887574082…88904885321496349601

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

3.843 × 10¹⁰²(103-digit number)

38435619837775148164…77809770642992699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.843 × 10¹⁰²(103-digit number)

38435619837775148164…77809770642992699201

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

7.687 × 10¹⁰²(103-digit number)

76871239675550296329…55619541285985398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.687 × 10¹⁰²(103-digit number)

76871239675550296329…55619541285985398401

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

1.537 × 10¹⁰³(104-digit number)

15374247935110059265…11239082571970796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.537 × 10¹⁰³(104-digit number)

15374247935110059265…11239082571970796801

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

3.074 × 10¹⁰³(104-digit number)

30748495870220118531…22478165143941593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.074 × 10¹⁰³(104-digit number)

30748495870220118531…22478165143941593601

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 #356,225

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