Block #1,534,821

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 12:03:04 PM · Difficulty 10.6186 · 5,281,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

45ccad8a24206dffc4e5d5afa7665bb3bdf107e1f5429c8df88b36795c7669aa

View on Chainz ↗

Height

#1,534,821

Difficulty

10.618648

Transactions

Size

7.60 KB

Version

Bits

0a9e5fb4

Nonce

378,924,831

Timestamp

4/10/2016, 12:03:04 PM

Confirmations

5,281,966

Mined by

⛏️ P2SHAXmuKvYKwGgnbCmBRiiGcb3y4ZootMc5Gn

Merkle Root

fb2454867857ba344bf80cc8b36f29be5e9a77b56e29727dbfa617434ee02723

Transactions (2)

Coinbasef8f2cf6b18f06c…c9e7c0a3986eb8

1 in → 1 out8.9300 XPM109 B

AXmuKvYK…ootMc5Gn

93dd2f14a4fbdd…cfec84add796c8

51 in → 1 out1532.4961 XPM7.41 KB

AUXoT8Na…FfJVQWSy

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.

5.191 × 10⁹³(94-digit number)

51913163692999613127…78300478061835418579

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

5.191 × 10⁹³(94-digit number)

51913163692999613127…78300478061835418579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.191 × 10⁹³(94-digit number)

51913163692999613127…78300478061835418581

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

1.038 × 10⁹⁴(95-digit number)

10382632738599922625…56600956123670837159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.038 × 10⁹⁴(95-digit number)

10382632738599922625…56600956123670837161

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

2.076 × 10⁹⁴(95-digit number)

20765265477199845251…13201912247341674319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.076 × 10⁹⁴(95-digit number)

20765265477199845251…13201912247341674321

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

4.153 × 10⁹⁴(95-digit number)

41530530954399690502…26403824494683348639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.153 × 10⁹⁴(95-digit number)

41530530954399690502…26403824494683348641

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

8.306 × 10⁹⁴(95-digit number)

83061061908799381004…52807648989366697279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.306 × 10⁹⁴(95-digit number)

83061061908799381004…52807648989366697281

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 #1,534,821

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