Block #324,399

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 7:27:23 AM · Difficulty 10.2073 · 6,474,717 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

324c0b320c326af158376ac48e77baf149bd1e1a55506c81937fec725b9177f4

View on Chainz ↗

Height

#324,399

Difficulty

10.207346

Transactions

Size

2.54 KB

Version

Bits

0a3514a0

Nonce

462,692

Timestamp

12/22/2013, 7:27:23 AM

Confirmations

6,474,717

Mined by

⛏️ aRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

89fb7d2941bbf2bfe61ccb594bdd9ac6c6bc274d71ecad1c883d683527293a66

Transactions (4)

Coinbase57622d29890606…19e5f18dec9715

1 in → 27 out9.5800 XPM981 B

AYcLTeXR…bscgPops Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 AP5UvYhU…vLTDwkdA

b1dd8e1235e1d8…fce7bfa7c88177

1 in → 2 out9.6100 XPM226 B

AZtgXUUG…hq8L7nCq ASohE1tM…YXY1mbeW

c7f19ea0f3f725…dbc732432aae32

7 in → 1 out2.2700 XPM1.05 KB

AHp3ZW4Q…7uiDHytp

8827c1bc8e7d13…4e68636e263749

1 in → 2 out6.5594 XPM225 B

AVCXQFU9…ndSyK98w APaeYaWu…U2Khhyo3

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.

5.842 × 10⁹⁸(99-digit number)

58425288067634277294…17484868768317712639

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

5.842 × 10⁹⁸(99-digit number)

58425288067634277294…17484868768317712639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.842 × 10⁹⁸(99-digit number)

58425288067634277294…17484868768317712641

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

1.168 × 10⁹⁹(100-digit number)

11685057613526855458…34969737536635425279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.168 × 10⁹⁹(100-digit number)

11685057613526855458…34969737536635425281

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

2.337 × 10⁹⁹(100-digit number)

23370115227053710917…69939475073270850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.337 × 10⁹⁹(100-digit number)

23370115227053710917…69939475073270850561

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

4.674 × 10⁹⁹(100-digit number)

46740230454107421835…39878950146541701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.674 × 10⁹⁹(100-digit number)

46740230454107421835…39878950146541701121

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

9.348 × 10⁹⁹(100-digit number)

93480460908214843670…79757900293083402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.348 × 10⁹⁹(100-digit number)

93480460908214843670…79757900293083402241

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