Block #2,132,168

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2017, 2:58:37 PM · Difficulty 10.9101 · 4,706,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c859ae11b9999e3fb299ca17bfb10cd35622c2fed0cb8a19bf624afae86afef9

View on Chainz ↗

Height

#2,132,168

Difficulty

10.910052

Transactions

Size

652 B

Version

Bits

0ae8f92b

Nonce

1,043,926,089

Timestamp

5/25/2017, 2:58:37 PM

Confirmations

4,706,128

Mined by

⛏️ P2SHAafmi1HUn3y8wvqfCCh9UJgzdTNme2f5DB

Merkle Root

d0055a8d618ed3a378704c0062205d39645d0d75c45fea68e1f9bb1b80234ed7

Transactions (3)

Coinbase4241ffdc515494…5c2a636dc9cb85

1 in → 1 out8.4100 XPM109 B

Aafmi1HU…Nme2f5DB

1ed192b68ceb13…d07ee9024a9f4b

1 in → 2 out43405.3750 XPM226 B

AdaLKx58…gAKEnziB AXDhTxNM…7byfa5ar

191aedf59122b7…582aa511a86998

1 in → 2 out42765.9339 XPM226 B

AM5iAcHi…EaSLASCq AL2KyDSz…Nce33jxg

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.

7.489 × 10⁹⁶(97-digit number)

74893243578065010713…39617503991728824319

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

7.489 × 10⁹⁶(97-digit number)

74893243578065010713…39617503991728824319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.489 × 10⁹⁶(97-digit number)

74893243578065010713…39617503991728824321

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

1.497 × 10⁹⁷(98-digit number)

14978648715613002142…79235007983457648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.497 × 10⁹⁷(98-digit number)

14978648715613002142…79235007983457648641

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

2.995 × 10⁹⁷(98-digit number)

29957297431226004285…58470015966915297279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.995 × 10⁹⁷(98-digit number)

29957297431226004285…58470015966915297281

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

5.991 × 10⁹⁷(98-digit number)

59914594862452008571…16940031933830594559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.991 × 10⁹⁷(98-digit number)

59914594862452008571…16940031933830594561

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

1.198 × 10⁹⁸(99-digit number)

11982918972490401714…33880063867661189119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.198 × 10⁹⁸(99-digit number)

11982918972490401714…33880063867661189121

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 #2,132,168

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