Block #323,036

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 9:48:53 AM · Difficulty 10.1980 · 6,484,931 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c308efe3b98c8ef2467fcbb346ebf8ecd258bb66dca645fd2e800f5663de952

View on Chainz ↗

Height

#323,036

Difficulty

10.198020

Transactions

Size

1003 B

Version

Bits

0a32b16e

Nonce

298,226

Timestamp

12/21/2013, 9:48:53 AM

Confirmations

6,484,931

Mined by

⛏️ aRcAdCzCa8uXjMmYxKADVGqq1rJfCaUQkKZ8z

Merkle Root

398a21d6eb7352cb730a442a739b2790c22f9dba43dc05583487aaa7a8ed8d81

Transactions (1)

Coinbase398a21d6eb7352…87aaa7a8ed8d81

1 in → 25 out9.6000 XPM912 B

AdCzCa8u…aUQkKZ8z Aac9Hjdg…P4ktypc3 AMbCuLHZ…WSoStwkc AbDHrhkn…fbZN1SRr AQ8QAT3J…rCFKuVbR

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.

1.003 × 10⁹⁷(98-digit number)

10035489170484758478…77942873694973843239

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

1.003 × 10⁹⁷(98-digit number)

10035489170484758478…77942873694973843239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.003 × 10⁹⁷(98-digit number)

10035489170484758478…77942873694973843241

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

2.007 × 10⁹⁷(98-digit number)

20070978340969516957…55885747389947686479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.007 × 10⁹⁷(98-digit number)

20070978340969516957…55885747389947686481

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

4.014 × 10⁹⁷(98-digit number)

40141956681939033915…11771494779895372959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.014 × 10⁹⁷(98-digit number)

40141956681939033915…11771494779895372961

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

8.028 × 10⁹⁷(98-digit number)

80283913363878067831…23542989559790745919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.028 × 10⁹⁷(98-digit number)

80283913363878067831…23542989559790745921

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

1.605 × 10⁹⁸(99-digit number)

16056782672775613566…47085979119581491839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.605 × 10⁹⁸(99-digit number)

16056782672775613566…47085979119581491841

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 #323,036

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