Block #1,524,586

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2016, 1:05:04 PM · Difficulty 10.6011 · 5,291,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4aaf5aebc344d06437e407bf23a77f2b0d130d0a7fe3d9340595a1c06723a1a7

View on Chainz ↗

Height

#1,524,586

Difficulty

10.601060

Transactions

Size

1.14 KB

Version

Bits

0a99df0f

Nonce

1,622,690,332

Timestamp

4/3/2016, 1:05:04 PM

Confirmations

5,291,574

Mined by

⛏️ P2SHANJrFLjGmLfnGk5fjkm1od9PBtyK8Y4F8X

Merkle Root

036854bc66192d6f8850c9c74db7e4a64f6083e9e23d0ca14d945451f742dcf6

Transactions (2)

Coinbase1cfbae0aea63fa…287012f3332ab2

1 in → 1 out8.8900 XPM109 B

ANJrFLjG…yK8Y4F8X

aef488d493e0c0…bf518658a0aa56

1 in → 24 out65.0381 XPM973 B

APGdziGW…3ou8jPJi ASLC3tFi…AeFMZHDv AaWqEybK…RQg7coeY AYCR3C12…mASeNwN5 AK7RAvSx…GCAgFMry

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.

4.556 × 10⁹⁴(95-digit number)

45561130110928418374…47115500912112599999

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

4.556 × 10⁹⁴(95-digit number)

45561130110928418374…47115500912112599999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.556 × 10⁹⁴(95-digit number)

45561130110928418374…47115500912112600001

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

9.112 × 10⁹⁴(95-digit number)

91122260221856836749…94231001824225199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.112 × 10⁹⁴(95-digit number)

91122260221856836749…94231001824225200001

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

1.822 × 10⁹⁵(96-digit number)

18224452044371367349…88462003648450399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.822 × 10⁹⁵(96-digit number)

18224452044371367349…88462003648450400001

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

3.644 × 10⁹⁵(96-digit number)

36448904088742734699…76924007296900799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.644 × 10⁹⁵(96-digit number)

36448904088742734699…76924007296900800001

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

7.289 × 10⁹⁵(96-digit number)

72897808177485469399…53848014593801599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.289 × 10⁹⁵(96-digit number)

72897808177485469399…53848014593801600001

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 #1,524,586

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