Block #591,075

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 6/16/2014, 6:47:46 PM · Difficulty 10.9452 · 6,221,668 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f175845124ce71c955f70f45b39e4d08ee2c818672dba91cfb4b2d190f2074d

View on Chainz ↗

Height

#591,075

Difficulty

10.945183

Transactions

Size

1.08 KB

Version

Bits

0af1f789

Nonce

2,429,588,814

Timestamp

6/16/2014, 6:47:46 PM

Confirmations

6,221,668

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4ea6f4782a8356934204faa83ed42ada0644065b79a8dbfe8633e815a48714ed

Transactions (2)

Coinbase2ec4b3c4005b15…61c1e4162dab9e

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

1e04b911b5afcb…c8a0eebce34af1

3 in → 13 out19.0313 XPM897 B

AUkdqaxr…4jcbMUQ7 Ab58ikyB…xcEYP1xG AKzv8KjF…W6FeM9j1 AJRwGPSP…QDRWdi2B AGfiKDEr…fmi54zvL

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.

2.277 × 10⁹⁸(99-digit number)

22773853032122966463…77055149852905059839

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

2.277 × 10⁹⁸(99-digit number)

22773853032122966463…77055149852905059839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.277 × 10⁹⁸(99-digit number)

22773853032122966463…77055149852905059841

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

4.554 × 10⁹⁸(99-digit number)

45547706064245932926…54110299705810119679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.554 × 10⁹⁸(99-digit number)

45547706064245932926…54110299705810119681

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

9.109 × 10⁹⁸(99-digit number)

91095412128491865852…08220599411620239359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.109 × 10⁹⁸(99-digit number)

91095412128491865852…08220599411620239361

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

1.821 × 10⁹⁹(100-digit number)

18219082425698373170…16441198823240478719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.821 × 10⁹⁹(100-digit number)

18219082425698373170…16441198823240478721

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

3.643 × 10⁹⁹(100-digit number)

36438164851396746341…32882397646480957439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.643 × 10⁹⁹(100-digit number)

36438164851396746341…32882397646480957441

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

7.287 × 10⁹⁹(100-digit number)

72876329702793492682…65764795292961914879

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

7.287 × 10⁹⁹(100-digit number)

72876329702793492682…65764795292961914881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #591,075

Cookie Preferences