Block #476,573

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 10:19:03 PM · Difficulty 10.4735 · 6,322,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eac879257b5f69442a4ac93620682b691be9a4c45ac04f5964cab6221bf13f21

View on Chainz ↗

Height

#476,573

Difficulty

10.473458

Transactions

Size

1.77 KB

Version

Bits

0a793492

Nonce

69,258

Timestamp

4/5/2014, 10:19:03 PM

Confirmations

6,322,361

Mined by

⛏️ EaS@AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

863e606f2dba10d7ab36447afc46a2640f593a1473f88c034356fa752552c640

Transactions (2)

Coinbase484563cf986395…5cf326483c2159

1 in → 24 out9.1000 XPM879 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

a1d4ee2e5749c3…6553dc82b7fbb6

4 in → 10 out28.0288 XPM839 B

AK3XRe91…xA8wva2G APGhKKy1…axmZARuS AJ1Rg4tk…5YkqEmTH AMLz4Dj6…KFvw5cVk Acn35Cbn…kDx6QvGN

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.

1.178 × 10⁹⁸(99-digit number)

11789430455229545862…44141194221513425919

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

1.178 × 10⁹⁸(99-digit number)

11789430455229545862…44141194221513425919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.178 × 10⁹⁸(99-digit number)

11789430455229545862…44141194221513425921

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

2.357 × 10⁹⁸(99-digit number)

23578860910459091725…88282388443026851839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.357 × 10⁹⁸(99-digit number)

23578860910459091725…88282388443026851841

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

4.715 × 10⁹⁸(99-digit number)

47157721820918183451…76564776886053703679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.715 × 10⁹⁸(99-digit number)

47157721820918183451…76564776886053703681

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

9.431 × 10⁹⁸(99-digit number)

94315443641836366902…53129553772107407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.431 × 10⁹⁸(99-digit number)

94315443641836366902…53129553772107407361

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

1.886 × 10⁹⁹(100-digit number)

18863088728367273380…06259107544214814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.886 × 10⁹⁹(100-digit number)

18863088728367273380…06259107544214814721

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