Block #2,118,611

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2017, 5:43:40 AM · Difficulty 10.9089 · 4,694,246 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ef193d59efa236bbd02a8692017551bf40fd47af087563c26bdf2faefa7b499

View on Chainz ↗

Height

#2,118,611

Difficulty

10.908870

Transactions

Size

3.05 KB

Version

Bits

0ae8abb7

Nonce

1,705,692,937

Timestamp

5/16/2017, 5:43:40 AM

Confirmations

4,694,246

Mined by

⛏️ P2SHAebVkoKdUM4aSRDCygqKkFGaVBj6k8JQsu

Merkle Root

00d7ab231564a83a560e72c4756bd292868790f78ad79bfbb6e41e1d9784de21

Transactions (2)

Coinbase12d314f2dd0d43…c63c27b4b159af

1 in → 1 out8.4200 XPM109 B

AebVkoKd…j6k8JQsu

aec8994936b319…a727cf991f3c47

19 in → 3 out677.9906 XPM2.85 KB

AWGzbFM3…3x69cHKp AU6SkzQn…PUiQp9Np ATkYRPjb…8y5c21Ay

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.

9.873 × 10⁹⁴(95-digit number)

98730145124501067862…68523727866103562239

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

9.873 × 10⁹⁴(95-digit number)

98730145124501067862…68523727866103562239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.873 × 10⁹⁴(95-digit number)

98730145124501067862…68523727866103562241

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

1.974 × 10⁹⁵(96-digit number)

19746029024900213572…37047455732207124479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.974 × 10⁹⁵(96-digit number)

19746029024900213572…37047455732207124481

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

3.949 × 10⁹⁵(96-digit number)

39492058049800427144…74094911464414248959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.949 × 10⁹⁵(96-digit number)

39492058049800427144…74094911464414248961

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

7.898 × 10⁹⁵(96-digit number)

78984116099600854289…48189822928828497919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.898 × 10⁹⁵(96-digit number)

78984116099600854289…48189822928828497921

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

1.579 × 10⁹⁶(97-digit number)

15796823219920170857…96379645857656995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.579 × 10⁹⁶(97-digit number)

15796823219920170857…96379645857656995841

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

Block #2,118,611

Cookie Preferences