Block #487,463

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 4:07:17 AM · Difficulty 10.6411 · 6,322,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acb4a1b52b66b5094dca03a9d518c060c375ed1419f668ec9c3be41705c5c1ed

View on Chainz ↗

Height

#487,463

Difficulty

10.641088

Transactions

Size

3.25 KB

Version

Bits

0aa41e60

Nonce

658,317,297

Timestamp

4/12/2014, 4:07:17 AM

Confirmations

6,322,385

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ca915c33434d7f6bcc42436b08223c2616a5074eb75c49590ec2b20bc37a3e0c

Transactions (3)

Coinbase78e09f6406989d…3c2776ab784e0d

1 in → 1 out8.8600 XPM116 B

AbwWkWZt…kawDhufa

f93f38f4b4685d…6bbe3586104a33

8 in → 2 out4.7171 XPM1.24 KB

ATDGPeQZ…KYSd7Per APF2RX8z…9YJSxKTW

00125189a372b4…3a6dfe96bba4a2

12 in → 2 out59.3637 XPM1.81 KB

AMX287i3…ts6SUx4f AMcMgvX1…7cfUzZRu

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.

1.120 × 10⁹⁹(100-digit number)

11201954540408371167…32118795907628083199

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

1.120 × 10⁹⁹(100-digit number)

11201954540408371167…32118795907628083199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.120 × 10⁹⁹(100-digit number)

11201954540408371167…32118795907628083201

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

2.240 × 10⁹⁹(100-digit number)

22403909080816742334…64237591815256166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.240 × 10⁹⁹(100-digit number)

22403909080816742334…64237591815256166401

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

4.480 × 10⁹⁹(100-digit number)

44807818161633484668…28475183630512332799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.480 × 10⁹⁹(100-digit number)

44807818161633484668…28475183630512332801

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

8.961 × 10⁹⁹(100-digit number)

89615636323266969337…56950367261024665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.961 × 10⁹⁹(100-digit number)

89615636323266969337…56950367261024665601

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

1.792 × 10¹⁰⁰(101-digit number)

17923127264653393867…13900734522049331199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.792 × 10¹⁰⁰(101-digit number)

17923127264653393867…13900734522049331201

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 #487,463

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