Block #2,153,343

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/9/2017, 2:42:35 PM · Difficulty 10.9031 · 4,671,687 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85e02c86964037e8fba06cda86c0be2a8f656704d1095ae941dae4651387c231

View on Chainz ↗

Height

#2,153,343

Difficulty

10.903062

Transactions

Size

1.11 KB

Version

Bits

0ae72f1a

Nonce

1,430,778,507

Timestamp

6/9/2017, 2:42:35 PM

Confirmations

4,671,687

Mined by

⛏️ P2SHAem93g3HhjnhXqVh1ssCLMo8xXN4v8ot5Q

Merkle Root

fe6e5b59dc15c97df9b7a92b8f284ad807cea69ec1ab684cc15cd4a2ad0180d5

Transactions (4)

Coinbase03494e916fdc34…723a59f7058292

1 in → 1 out8.4300 XPM110 B

Aem93g3H…N4v8ot5Q

c97373611c0722…5e4b2ab6c40f1b

2 in → 2 out10.7643 XPM341 B

AU54G61D…frFBuv4o AYiVkR5s…Waom7bcN

5ad788fc99ffc9…66b8d1e56d4f36

1 in → 2 out4.2416 XPM225 B

ANwtSRNc…za9KnLoD AGKp8fKQ…1dhZb99N

964cd9fa7b85aa…2ba91407574c75

2 in → 2 out4.3770 XPM374 B

ASdXKexa…kch59HW5 ALro3yLZ…YKRAAsQm

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.

7.041 × 10⁹⁴(95-digit number)

70415328502036265251…38866549834753278719

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

7.041 × 10⁹⁴(95-digit number)

70415328502036265251…38866549834753278719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.041 × 10⁹⁴(95-digit number)

70415328502036265251…38866549834753278721

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

1.408 × 10⁹⁵(96-digit number)

14083065700407253050…77733099669506557439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.408 × 10⁹⁵(96-digit number)

14083065700407253050…77733099669506557441

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

2.816 × 10⁹⁵(96-digit number)

28166131400814506100…55466199339013114879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.816 × 10⁹⁵(96-digit number)

28166131400814506100…55466199339013114881

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

5.633 × 10⁹⁵(96-digit number)

56332262801629012201…10932398678026229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.633 × 10⁹⁵(96-digit number)

56332262801629012201…10932398678026229761

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

1.126 × 10⁹⁶(97-digit number)

11266452560325802440…21864797356052459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.126 × 10⁹⁶(97-digit number)

11266452560325802440…21864797356052459521

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

2.253 × 10⁹⁶(97-digit number)

22532905120651604880…43729594712104919039

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 #2,153,343

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