Block #119,026

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/16/2013, 4:59:45 AM · Difficulty 9.7493 · 6,683,912 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a4f1a81ed1a22ee882614e60c96cceb7f5c68de4f488278d50d9736128c8856

View on Chainz ↗

Height

#119,026

Difficulty

9.749302

Transactions

Size

359 B

Version

Bits

09bfd245

Nonce

273,379

Timestamp

8/16/2013, 4:59:45 AM

Confirmations

6,683,912

Mined by

⛏️ P2SHAYyPPXgF5A3RKbdbyWYgDSxAkdb6nr5cD2

Merkle Root

3a5d3ce2ce1e8dfd7de3d25fcb78857ecb80d5f9c1efed6714709973caacea89

Transactions (2)

Coinbase3a96f51ba494ed…67fee86626cc03

1 in → 1 out10.5200 XPM109 B

AYyPPXgF…b6nr5cD2

de8a6ad8dc2afe…30e37a8d7b4716

1 in → 1 out10.5600 XPM159 B

AKfeR8gS…LNjUzaey

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.

6.507 × 10⁹⁷(98-digit number)

65075040684297680020…39974983136574933019

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

6.507 × 10⁹⁷(98-digit number)

65075040684297680020…39974983136574933019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.507 × 10⁹⁷(98-digit number)

65075040684297680020…39974983136574933021

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

1.301 × 10⁹⁸(99-digit number)

13015008136859536004…79949966273149866039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.301 × 10⁹⁸(99-digit number)

13015008136859536004…79949966273149866041

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

2.603 × 10⁹⁸(99-digit number)

26030016273719072008…59899932546299732079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.603 × 10⁹⁸(99-digit number)

26030016273719072008…59899932546299732081

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

5.206 × 10⁹⁸(99-digit number)

52060032547438144016…19799865092599464159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.206 × 10⁹⁸(99-digit number)

52060032547438144016…19799865092599464161

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

1.041 × 10⁹⁹(100-digit number)

10412006509487628803…39599730185198928319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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