Block #1,590,626

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/18/2016, 10:03:47 PM · Difficulty 10.6561 · 5,250,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d313c8015a0f81e25c856d34064ef3bebb3ae13702cbfaa6c80db8f934826913

View on Chainz ↗

Height

#1,590,626

Difficulty

10.656057

Transactions

Size

935 B

Version

Bits

0aa7f359

Nonce

1,031,491,338

Timestamp

5/18/2016, 10:03:47 PM

Confirmations

5,250,527

Mined by

⛏️ P2SHAM7hnHAgBxTLcDZb24s23R6S8dnHwkCynU

Merkle Root

cd2d1b1feb20205b4d2a41096edd02e639aedc9e43880901f1d86f547e63e8ef

Transactions (2)

Coinbase3523a63a0b27b9…eafe311848fce6

1 in → 1 out8.8000 XPM109 B

AM7hnHAg…nHwkCynU

bb0ed81089edb5…e497745f598479

1 in → 17 out168.9174 XPM736 B

AHcAWgq6…1KqE2twc AJU9L2KC…pYwsyY47 Abd5J1Un…n4wGjECx AVbPDrE9…qY1ei75k AKYqpStf…khGBwMfc

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.

2.305 × 10⁹⁴(95-digit number)

23054183044443176528…12324540530598214399

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

2.305 × 10⁹⁴(95-digit number)

23054183044443176528…12324540530598214399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.305 × 10⁹⁴(95-digit number)

23054183044443176528…12324540530598214401

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

4.610 × 10⁹⁴(95-digit number)

46108366088886353056…24649081061196428799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.610 × 10⁹⁴(95-digit number)

46108366088886353056…24649081061196428801

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

9.221 × 10⁹⁴(95-digit number)

92216732177772706112…49298162122392857599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.221 × 10⁹⁴(95-digit number)

92216732177772706112…49298162122392857601

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

1.844 × 10⁹⁵(96-digit number)

18443346435554541222…98596324244785715199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.844 × 10⁹⁵(96-digit number)

18443346435554541222…98596324244785715201

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

3.688 × 10⁹⁵(96-digit number)

36886692871109082444…97192648489571430399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.688 × 10⁹⁵(96-digit number)

36886692871109082444…97192648489571430401

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 #1,590,626

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