Block #458,521

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 3:59:14 PM · Difficulty 10.4203 · 6,346,754 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3bb0ec9aca1b7d0bf38b3dad911b986d85f2e7500729bbbef15330a03acf5b51

View on Chainz ↗

Height

#458,521

Difficulty

10.420286

Transactions

Size

948 B

Version

Bits

0a6b97da

Nonce

506,688

Timestamp

3/24/2014, 3:59:14 PM

Confirmations

6,346,754

Mined by

⛏️ P2SHAYEzJq7kUZYtKDXvpghi5q28zx7DzDky4R

Merkle Root

6ab8846f5f34ea5773145d4075133c7035d38c633ab27e94e6fdc17f94967254

Transactions (3)

Coinbaseff36fdc41b4339…e9225ef84bd573

1 in → 1 out9.2200 XPM109 B

AYEzJq7k…7DzDky4R

4569afa5f612d8…c55273b5c4934a

1 in → 2 out5.7566 XPM226 B

AdFhKNHL…63WWoeJY AGCmTSw4…QNSsCSPC

6bce3ffb252903…88ee915aa309cf

3 in → 2 out1.1000 XPM523 B

AenpbxNn…AL481VM9 AXnL68UR…jsxeGUhN

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.

1.803 × 10⁹⁵(96-digit number)

18037732369289242690…06424960848781248039

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

1.803 × 10⁹⁵(96-digit number)

18037732369289242690…06424960848781248039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.803 × 10⁹⁵(96-digit number)

18037732369289242690…06424960848781248041

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

3.607 × 10⁹⁵(96-digit number)

36075464738578485380…12849921697562496079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.607 × 10⁹⁵(96-digit number)

36075464738578485380…12849921697562496081

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

7.215 × 10⁹⁵(96-digit number)

72150929477156970760…25699843395124992159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.215 × 10⁹⁵(96-digit number)

72150929477156970760…25699843395124992161

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

1.443 × 10⁹⁶(97-digit number)

14430185895431394152…51399686790249984319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.443 × 10⁹⁶(97-digit number)

14430185895431394152…51399686790249984321

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

2.886 × 10⁹⁶(97-digit number)

28860371790862788304…02799373580499968639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.886 × 10⁹⁶(97-digit number)

28860371790862788304…02799373580499968641

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