Block #365,651

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 9:59:25 PM · Difficulty 10.4135 · 6,437,016 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3674953c078add5a9472b7371160a5f7d0b64962dd38f827cfd19031fe6e384b

View on Chainz ↗

Height

#365,651

Difficulty

10.413497

Transactions

Size

732 B

Version

Bits

0a69daea

Nonce

13,638

Timestamp

1/18/2014, 9:59:25 PM

Confirmations

6,437,016

Mined by

⛏️ SAM4c6u8dYeQBkdo3RbtZ8WqY8DwUNSLEd4

Merkle Root

afe89151e6cfd7e6b610a47d1f949885d050b1aacab1dcd8c4b93030e6f02e56

Transactions (1)

Coinbaseafe89151e6cfd7…b93030e6f02e56

1 in → 17 out9.2100 XPM641 B

AM4c6u8d…wUNSLEd4 AFutDVqJ…TJTJj6UF APFsQ3Fo…xoFKrF12 AMHMrUuK…jgEj6HLr AczyTBWn…bEQQj33u

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.

2.590 × 10⁹⁷(98-digit number)

25905050717759532204…47440720528024755199

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

2.590 × 10⁹⁷(98-digit number)

25905050717759532204…47440720528024755199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.590 × 10⁹⁷(98-digit number)

25905050717759532204…47440720528024755201

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

5.181 × 10⁹⁷(98-digit number)

51810101435519064408…94881441056049510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.181 × 10⁹⁷(98-digit number)

51810101435519064408…94881441056049510401

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

1.036 × 10⁹⁸(99-digit number)

10362020287103812881…89762882112099020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.036 × 10⁹⁸(99-digit number)

10362020287103812881…89762882112099020801

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

2.072 × 10⁹⁸(99-digit number)

20724040574207625763…79525764224198041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.072 × 10⁹⁸(99-digit number)

20724040574207625763…79525764224198041601

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

4.144 × 10⁹⁸(99-digit number)

41448081148415251527…59051528448396083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.144 × 10⁹⁸(99-digit number)

41448081148415251527…59051528448396083201

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