Block #1,355,619

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2015, 10:38:57 AM · Difficulty 10.8139 · 5,436,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5b2888495d5cf94b1049791921d1df0cbc8de42e8af6465d588df44c78a6e2a

View on Chainz ↗

Height

#1,355,619

Difficulty

10.813927

Transactions

Size

1.29 KB

Version

Bits

0ad05d84

Nonce

141,362,756

Timestamp

12/5/2015, 10:38:57 AM

Confirmations

5,436,052

Merkle Root

efaf818b9e1d1a3dc7f6ee0259eda1a2d79bb1fd609b187c9176967b449225db

Transactions (4)

Coinbasef9b7d22652189b…0e0f6966f9cf79

1 in → 1 out8.5700 XPM110 B

AMqotLsj…Kq46LE8m

a847e590d4991c…f30a01b9af6953

1 in → 2 out8.4400 XPM227 B

AQtisFei…VwsPGKH9 AbJgk664…KyH1W9Ba

ce98ebdfdb979a…ce774cd083531b

1 in → 2 out4.1146 XPM227 B

AeCpbgWf…aDdoebpK AcuM7XiJ…5uND8Jce

4cdcdcb84ba287…42b634843ffcb3

4 in → 2 out1.0541 XPM669 B

AZbmtFjN…owcdaqGy AUkQ1xqi…ducy55wE

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.

2.597 × 10⁹⁷(98-digit number)

25971630124085204569…33209947343765432319

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

2.597 × 10⁹⁷(98-digit number)

25971630124085204569…33209947343765432319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.597 × 10⁹⁷(98-digit number)

25971630124085204569…33209947343765432321

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

5.194 × 10⁹⁷(98-digit number)

51943260248170409138…66419894687530864639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.194 × 10⁹⁷(98-digit number)

51943260248170409138…66419894687530864641

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

1.038 × 10⁹⁸(99-digit number)

10388652049634081827…32839789375061729279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.038 × 10⁹⁸(99-digit number)

10388652049634081827…32839789375061729281

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

2.077 × 10⁹⁸(99-digit number)

20777304099268163655…65679578750123458559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.077 × 10⁹⁸(99-digit number)

20777304099268163655…65679578750123458561

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

4.155 × 10⁹⁸(99-digit number)

41554608198536327310…31359157500246917119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.155 × 10⁹⁸(99-digit number)

41554608198536327310…31359157500246917121

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