Block #459,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2014, 3:26:33 AM · Difficulty 10.4172 · 6,347,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27ffd1f0a73c9b9d5dfaf73af762d8cc9b4d67919216a249aeca357ba207e8af

View on Chainz ↗

Height

#459,179

Difficulty

10.417170

Transactions

Size

58.24 KB

Version

Bits

0a6acba1

Nonce

37,354

Timestamp

3/25/2014, 3:26:33 AM

Confirmations

6,347,131

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

db416847bae44940caa04dc51fab733df58e2155ec199c1807d07b13b6cbe997

Transactions (5)

Coinbase1a6ec1b29c2c22…7fde4c6e54334d

1 in → 1 out9.8200 XPM116 B

AbwWkWZt…kawDhufa

a2afea6ee58aa1…e4ceceefe9884e

95 in → 2 out50.0100 XPM13.81 KB

Acw8wrQ5…csMyvZfu AenngGyp…XDXq3hCS

3eea5ccc3433bd…57f599758fe5f2

4 in → 12 out36.9100 XPM876 B

ATftMu9h…u1bnoiYw ASEVuzfF…Kzim7qGy ARrEVN6m…zWjT6LC4 AZSGfpD4…s4aWX4R1 AXA2CgAY…sjcwKJeP

4d35ffede96ab0…8457b12eae722b

298 in → 2 out500.0100 XPM43.16 KB

AJjnK9uC…VreFquR4 AZCGKknd…spP25yY3

438744ceeeb13d…c8f884fd9a6ad8

1 in → 2 out2.0797 XPM227 B

AcS2LG5b…cHmt95Ut AK3w3Tet…vVZHU7hU

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.

9.355 × 10⁹⁴(95-digit number)

93558212633018910348…99473177361997212159

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

9.355 × 10⁹⁴(95-digit number)

93558212633018910348…99473177361997212159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.355 × 10⁹⁴(95-digit number)

93558212633018910348…99473177361997212161

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

1.871 × 10⁹⁵(96-digit number)

18711642526603782069…98946354723994424319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.871 × 10⁹⁵(96-digit number)

18711642526603782069…98946354723994424321

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

3.742 × 10⁹⁵(96-digit number)

37423285053207564139…97892709447988848639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.742 × 10⁹⁵(96-digit number)

37423285053207564139…97892709447988848641

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

7.484 × 10⁹⁵(96-digit number)

74846570106415128278…95785418895977697279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.484 × 10⁹⁵(96-digit number)

74846570106415128278…95785418895977697281

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

1.496 × 10⁹⁶(97-digit number)

14969314021283025655…91570837791955394559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.496 × 10⁹⁶(97-digit number)

14969314021283025655…91570837791955394561

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 #459,179

Cookie Preferences