Block #482,387

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 11:20:13 AM · Difficulty 10.5445 · 6,325,428 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

398ea96d630251fd3627125b72946ef92e31f17e41e544a98ebc2326953081ee

View on Chainz ↗

Height

#482,387

Difficulty

10.544544

Transactions

Size

972 B

Version

Bits

0a8b673b

Nonce

11,578

Timestamp

4/9/2014, 11:20:13 AM

Confirmations

6,325,428

Mined by

⛏️ S\aSE,8AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

06d05591cfe8dbeb5141584014b98d2c66bc6229fbd991de4d6f54aff199e42f

Transactions (1)

Coinbase06d05591cfe8db…6f54aff199e42f

1 in → 24 out8.9800 XPM879 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1

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.

2.081 × 10¹⁰¹(102-digit number)

20811097717890300455…77105632997158523199

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

2.081 × 10¹⁰¹(102-digit number)

20811097717890300455…77105632997158523199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.081 × 10¹⁰¹(102-digit number)

20811097717890300455…77105632997158523201

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

4.162 × 10¹⁰¹(102-digit number)

41622195435780600910…54211265994317046399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.162 × 10¹⁰¹(102-digit number)

41622195435780600910…54211265994317046401

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

8.324 × 10¹⁰¹(102-digit number)

83244390871561201820…08422531988634092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.324 × 10¹⁰¹(102-digit number)

83244390871561201820…08422531988634092801

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

1.664 × 10¹⁰²(103-digit number)

16648878174312240364…16845063977268185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.664 × 10¹⁰²(103-digit number)

16648878174312240364…16845063977268185601

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

3.329 × 10¹⁰²(103-digit number)

33297756348624480728…33690127954536371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.329 × 10¹⁰²(103-digit number)

33297756348624480728…33690127954536371201

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 #482,387

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