Block #506,567

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 4:28:51 AM · Difficulty 10.8139 · 6,302,285 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c3826b0946246a3973d11e11be5c6b257534562e6df436d10b129e941f1b7f2

View on Chainz ↗

Height

#506,567

Difficulty

10.813876

Transactions

Size

3.57 KB

Version

Bits

0ad05a33

Nonce

391,531

Timestamp

4/23/2014, 4:28:51 AM

Confirmations

6,302,285

Mined by

⛏️ aSWA6AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9639e668aab6a418f234e5a363cd92a4dc687ff0008de4c5b3bc9fa0bf95b6db

Transactions (4)

Coinbase1711bfcc0a7ff8…eef1644fd03e2d

1 in → 18 out8.5400 XPM675 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 AJzWx2VD…j4ZSMit5 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1

d566a33f8cd728…a6cf1b8cc4f9ca

16 in → 2 out46.1052 XPM2.38 KB

AKwYQQYZ…5jmeyi4z Aaq5ydQe…MWD3ZPck

eb8767ea55e8df…0f789064b910d1

1 in → 2 out1.8879 XPM225 B

AMHSrSJQ…F3ziNLML AG8u7ddV…cU5QJSqk

3b043979c7bd1f…5eb41fb0089d24

1 in → 2 out1.1434 XPM225 B

AVDduQo6…BkNfKzER APes4uNP…74RuLjMh

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.

4.585 × 10⁹³(94-digit number)

45851278246927518202…03628347504072447999

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

4.585 × 10⁹³(94-digit number)

45851278246927518202…03628347504072447999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.585 × 10⁹³(94-digit number)

45851278246927518202…03628347504072448001

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

9.170 × 10⁹³(94-digit number)

91702556493855036404…07256695008144895999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.170 × 10⁹³(94-digit number)

91702556493855036404…07256695008144896001

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

1.834 × 10⁹⁴(95-digit number)

18340511298771007280…14513390016289791999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.834 × 10⁹⁴(95-digit number)

18340511298771007280…14513390016289792001

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

3.668 × 10⁹⁴(95-digit number)

36681022597542014561…29026780032579583999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.668 × 10⁹⁴(95-digit number)

36681022597542014561…29026780032579584001

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

7.336 × 10⁹⁴(95-digit number)

73362045195084029123…58053560065159167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.336 × 10⁹⁴(95-digit number)

73362045195084029123…58053560065159168001

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 #506,567

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