Block #1,889,417

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2016, 5:47:04 PM · Difficulty 10.7274 · 4,927,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f1088677adfa7939f5a6408d8064e92d8ac48085bb6a81ce1bd5f03aaa56210

View on Chainz ↗

Height

#1,889,417

Difficulty

10.727438

Transactions

Size

984 B

Version

Bits

0aba3962

Nonce

753,907,959

Timestamp

12/11/2016, 5:47:04 PM

Confirmations

4,927,715

Mined by

⛏️ P2SHAPWfcVBYEg6qcQsnkEB6WuFM8SAxJFikzt

Merkle Root

ba1fa58baa4b13f7a482c55b01a1f10a00cb0d375df8b1efdbe9096df15df67a

Transactions (2)

Coinbase3d672868ac96fa…122698c9c443ed

1 in → 1 out8.6900 XPM110 B

APWfcVBY…AxJFikzt

fb84b04194faf0…289d878aa4d952

5 in → 1 out129.8227 XPM785 B

AcTfQfkA…gCuFSnFt

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.

2.627 × 10⁹²(93-digit number)

26278060971445418324…49836961127332391259

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

2.627 × 10⁹²(93-digit number)

26278060971445418324…49836961127332391259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.627 × 10⁹²(93-digit number)

26278060971445418324…49836961127332391261

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

5.255 × 10⁹²(93-digit number)

52556121942890836649…99673922254664782519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.255 × 10⁹²(93-digit number)

52556121942890836649…99673922254664782521

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

1.051 × 10⁹³(94-digit number)

10511224388578167329…99347844509329565039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.051 × 10⁹³(94-digit number)

10511224388578167329…99347844509329565041

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

2.102 × 10⁹³(94-digit number)

21022448777156334659…98695689018659130079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.102 × 10⁹³(94-digit number)

21022448777156334659…98695689018659130081

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

4.204 × 10⁹³(94-digit number)

42044897554312669319…97391378037318260159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.204 × 10⁹³(94-digit number)

42044897554312669319…97391378037318260161

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 #1,889,417

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