Block #2,134,797

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/27/2017, 2:33:03 PM · Difficulty 10.9060 · 4,705,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f064eb29f8d819645e3f130d8e1f4d042ade4f42d35425f3224fb1f5e4ee3a2c

View on Chainz ↗

Height

#2,134,797

Difficulty

10.906040

Transactions

Size

3.21 KB

Version

Bits

0ae7f23b

Nonce

1,447,562,291

Timestamp

5/27/2017, 2:33:03 PM

Confirmations

4,705,326

Mined by

⛏️ P2SHASdLESCDurEmP6pH1gNni6S3y4pAjD8ySP

Merkle Root

bee418a5f256892c16369c070d81d02946ae392131365636fc25882ac852183c

Transactions (3)

Coinbase5e0e54be2cdad2…2ec5addfb1a7bd

1 in → 1 out8.4300 XPM109 B

ASdLESCD…pAjD8ySP

d3330d59847255…ea5bb452570a1e

2 in → 2 out166.8000 XPM372 B

AUoPaiLi…z4AtGRoX AN8TKRod…EESchqAK

084c9658238daf…591aafc0e4fffe

18 in → 1 out103.9700 XPM2.65 KB

AZE4Pwgy…KNsYdSoQ

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.

6.796 × 10⁹⁵(96-digit number)

67962074289007899812…90615869537761739519

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

6.796 × 10⁹⁵(96-digit number)

67962074289007899812…90615869537761739519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.796 × 10⁹⁵(96-digit number)

67962074289007899812…90615869537761739521

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

1.359 × 10⁹⁶(97-digit number)

13592414857801579962…81231739075523479039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.359 × 10⁹⁶(97-digit number)

13592414857801579962…81231739075523479041

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

2.718 × 10⁹⁶(97-digit number)

27184829715603159924…62463478151046958079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.718 × 10⁹⁶(97-digit number)

27184829715603159924…62463478151046958081

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

5.436 × 10⁹⁶(97-digit number)

54369659431206319849…24926956302093916159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.436 × 10⁹⁶(97-digit number)

54369659431206319849…24926956302093916161

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

1.087 × 10⁹⁷(98-digit number)

10873931886241263969…49853912604187832319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.087 × 10⁹⁷(98-digit number)

10873931886241263969…49853912604187832321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.174 × 10⁹⁷(98-digit number)

21747863772482527939…99707825208375664639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,134,797

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