Block #2,641,850

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 12:26:09 PM · Difficulty 11.6339 · 4,190,028 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b357eec181a9ff2bdd35c3c2fc2717982b6f65801bd1a0fb931b93012206a92e

View on Chainz ↗

Height

#2,641,850

Difficulty

11.633949

Transactions

Size

1.15 KB

Version

Bits

0ba24a77

Nonce

418,178,624

Timestamp

5/1/2018, 12:26:09 PM

Confirmations

4,190,028

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e409a2221319e7b6c05d3edfd80557bd5b83ae7f65ed358aed38d502606a9b96

Transactions (4)

Coinbaseaea993128a7dc1…1bf5b00f4a3f30

1 in → 1 out7.4100 XPM110 B

Adqah8zh…1WwoHJ9t

026232977b1822…abd72c8feb8a55

1 in → 2 out6.4472 XPM226 B

AVts9MY4…UHzoGngY AMjZ87GH…cvurqAXE

9dd179fb4acf72…71a5f1ebb34385

1 in → 2 out1.4671 XPM226 B

AZBGBBQd…ExqEYGNc AHpyoM9a…fR4QRCwh

edb0e2597a2639…0a89612a0ccdad

3 in → 2 out0.0688 XPM522 B

AZBGBBQd…ExqEYGNc AK5j9ujB…A6XHh1YV

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.

1.309 × 10⁹⁷(98-digit number)

13094496417522550491…74714335836385459199

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

1.309 × 10⁹⁷(98-digit number)

13094496417522550491…74714335836385459199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.309 × 10⁹⁷(98-digit number)

13094496417522550491…74714335836385459201

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

2.618 × 10⁹⁷(98-digit number)

26188992835045100982…49428671672770918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.618 × 10⁹⁷(98-digit number)

26188992835045100982…49428671672770918401

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

5.237 × 10⁹⁷(98-digit number)

52377985670090201965…98857343345541836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.237 × 10⁹⁷(98-digit number)

52377985670090201965…98857343345541836801

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

1.047 × 10⁹⁸(99-digit number)

10475597134018040393…97714686691083673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.047 × 10⁹⁸(99-digit number)

10475597134018040393…97714686691083673601

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

2.095 × 10⁹⁸(99-digit number)

20951194268036080786…95429373382167347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.095 × 10⁹⁸(99-digit number)

20951194268036080786…95429373382167347201

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

4.190 × 10⁹⁸(99-digit number)

41902388536072161572…90858746764334694399

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 #2,641,850

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