Block #2,943,413

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/28/2018, 7:18:13 PM · Difficulty 11.3949 · 3,898,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6486064dcd9e30d04980416374c8590b71bf7731233a565b28c7fc9e9854689b

View on Chainz ↗

Height

#2,943,413

Difficulty

11.394928

Transactions

Size

872 B

Version

Bits

0b651a07

Nonce

953,225,521

Timestamp

11/28/2018, 7:18:13 PM

Confirmations

3,898,074

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

1351bf76f780b7da57d6566cc543db55a8b58b6286f5fbe70fa3476fb7b1696d

Transactions (2)

Coinbasec1d4ae6330a003…33337d1385d0d1

1 in → 1 out7.7100 XPM110 B

AbXwmGxD…4XXYP765

6ed88572647df2…4316e5c96282e6

4 in → 2 out783.0100 XPM670 B

AbKsgpKm…meMyn6QD AZUcY9LX…ZGdFeK5w

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.

2.226 × 10⁹⁸(99-digit number)

22265792821762644534…91676048224043007999

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

2.226 × 10⁹⁸(99-digit number)

22265792821762644534…91676048224043007999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.226 × 10⁹⁸(99-digit number)

22265792821762644534…91676048224043008001

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

4.453 × 10⁹⁸(99-digit number)

44531585643525289068…83352096448086015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.453 × 10⁹⁸(99-digit number)

44531585643525289068…83352096448086016001

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

8.906 × 10⁹⁸(99-digit number)

89063171287050578137…66704192896172031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.906 × 10⁹⁸(99-digit number)

89063171287050578137…66704192896172032001

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

1.781 × 10⁹⁹(100-digit number)

17812634257410115627…33408385792344063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.781 × 10⁹⁹(100-digit number)

17812634257410115627…33408385792344064001

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

3.562 × 10⁹⁹(100-digit number)

35625268514820231254…66816771584688127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.562 × 10⁹⁹(100-digit number)

35625268514820231254…66816771584688128001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.125 × 10⁹⁹(100-digit number)

71250537029640462509…33633543169376255999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,943,413

Cookie Preferences