Block #2,051,988

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2017, 5:06:58 PM · Difficulty 10.7299 · 4,790,936 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6cb39fccae3a32f38b0c67ff01674cca72a7453cfda90b37a74476959ac335ad

View on Chainz ↗

Height

#2,051,988

Difficulty

10.729945

Transactions

Size

652 B

Version

Bits

0abaddad

Nonce

1,166,332,129

Timestamp

4/3/2017, 5:06:58 PM

Confirmations

4,790,936

Mined by

⛏️ P2SHAbbnAH6Y3Ze7x1ircP3rL4ALX8iBAJcvcg

Merkle Root

5d3feafd16ba77b126e35f3f56154844d4e304797c079ffd75cb3192ddf29174

Transactions (3)

Coinbase9adf20870b4260…fda1a4a8bc2a62

1 in → 1 out8.6900 XPM110 B

AbbnAH6Y…iBAJcvcg

f6bde9c5dc8e44…d03d6ba68b344c

1 in → 2 out56290.2019 XPM226 B

AGnt7L1U…TNRZjmDf AYed75Xe…ze8unUtP

23e5e4b1398282…acfdae752924ed

1 in → 2 out56242.6719 XPM226 B

AZMaKVC9…TLZ3oKvL APF9EEWK…PK2CjXxB

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.

5.280 × 10⁹⁵(96-digit number)

52800448397004129226…93884153040275014079

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

5.280 × 10⁹⁵(96-digit number)

52800448397004129226…93884153040275014079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.280 × 10⁹⁵(96-digit number)

52800448397004129226…93884153040275014081

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

1.056 × 10⁹⁶(97-digit number)

10560089679400825845…87768306080550028159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.056 × 10⁹⁶(97-digit number)

10560089679400825845…87768306080550028161

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

2.112 × 10⁹⁶(97-digit number)

21120179358801651690…75536612161100056319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.112 × 10⁹⁶(97-digit number)

21120179358801651690…75536612161100056321

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

4.224 × 10⁹⁶(97-digit number)

42240358717603303381…51073224322200112639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.224 × 10⁹⁶(97-digit number)

42240358717603303381…51073224322200112641

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

8.448 × 10⁹⁶(97-digit number)

84480717435206606763…02146448644400225279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.448 × 10⁹⁶(97-digit number)

84480717435206606763…02146448644400225281

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 #2,051,988

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