Block #1,482,363

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2016, 9:06:56 PM · Difficulty 10.7269 · 5,351,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7200ff3269ac15d86e6da1c70ea553589f74d14e80338b3d89da485f75d3fdd0

View on Chainz ↗

Height

#1,482,363

Difficulty

10.726936

Transactions

Size

1.45 KB

Version

Bits

0aba1882

Nonce

61,855,105

Timestamp

3/3/2016, 9:06:56 PM

Confirmations

5,351,143

Mined by

⛏️ P2SHAXtBJueyka3ASeBHkMicbFbmUjopfbSa6a

Merkle Root

01d7d29e70feb027eeb90d28013714066b8e391f791b3b533629b49c4cc2eeea

Transactions (2)

Coinbase3aaa940a953693…68a62cc85969c2

1 in → 1 out8.7000 XPM110 B

AXtBJuey…opfbSa6a

d3e163e4cf55ab…bd5ad55f45f8c5

1 in → 33 out144.5364 XPM1.25 KB

AHLkr8VW…72s1bCzw AK7RAvSx…GCAgFMry Ae6hzvbG…gykFPKYM AaTP6ovb…rYJuQEfo Ab3XajLC…mffKcJsF

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.

4.386 × 10⁹⁴(95-digit number)

43864788898428315327…74554860319372397599

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

4.386 × 10⁹⁴(95-digit number)

43864788898428315327…74554860319372397599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.386 × 10⁹⁴(95-digit number)

43864788898428315327…74554860319372397601

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

8.772 × 10⁹⁴(95-digit number)

87729577796856630654…49109720638744795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.772 × 10⁹⁴(95-digit number)

87729577796856630654…49109720638744795201

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

1.754 × 10⁹⁵(96-digit number)

17545915559371326130…98219441277489590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.754 × 10⁹⁵(96-digit number)

17545915559371326130…98219441277489590401

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

3.509 × 10⁹⁵(96-digit number)

35091831118742652261…96438882554979180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.509 × 10⁹⁵(96-digit number)

35091831118742652261…96438882554979180801

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

7.018 × 10⁹⁵(96-digit number)

70183662237485304523…92877765109958361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.018 × 10⁹⁵(96-digit number)

70183662237485304523…92877765109958361601

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 #1,482,363

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