Block #524,457

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/4/2014, 4:58:59 AM · Difficulty 10.8760 · 6,286,526 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d4822dd0d07f747d6f2241beec7ba866d7e7195066f8d6f7a398283a8cb73c1

View on Chainz ↗

Height

#524,457

Difficulty

10.875985

Transactions

Size

800 B

Version

Bits

0ae04088

Nonce

13,001

Timestamp

5/4/2014, 4:58:59 AM

Confirmations

6,286,526

Mined by

⛏️ aSeAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1b8ce5214f5c347da369665eb662c24aa93445469fc794597f44cc4a9b821d93

Transactions (1)

Coinbase1b8ce5214f5c34…44cc4a9b821d93

1 in → 19 out8.4400 XPM709 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ

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.

6.060 × 10⁹⁷(98-digit number)

60603691969318427226…96801152049936537599

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

6.060 × 10⁹⁷(98-digit number)

60603691969318427226…96801152049936537599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.060 × 10⁹⁷(98-digit number)

60603691969318427226…96801152049936537601

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

1.212 × 10⁹⁸(99-digit number)

12120738393863685445…93602304099873075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.212 × 10⁹⁸(99-digit number)

12120738393863685445…93602304099873075201

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

2.424 × 10⁹⁸(99-digit number)

24241476787727370890…87204608199746150399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.424 × 10⁹⁸(99-digit number)

24241476787727370890…87204608199746150401

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

4.848 × 10⁹⁸(99-digit number)

48482953575454741780…74409216399492300799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.848 × 10⁹⁸(99-digit number)

48482953575454741780…74409216399492300801

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

9.696 × 10⁹⁸(99-digit number)

96965907150909483561…48818432798984601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.696 × 10⁹⁸(99-digit number)

96965907150909483561…48818432798984601601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.939 × 10⁹⁹(100-digit number)

19393181430181896712…97636865597969203199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #524,457

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