Block #2,292,893

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/12/2017, 2:53:33 AM · Difficulty 10.9548 · 4,550,718 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7eb2c7229dd27d4201ae28ca447aab468bd6504b53cbd252b46e7e98a77a6e77

View on Chainz ↗

Height

#2,292,893

Difficulty

10.954814

Transactions

Size

652 B

Version

Bits

0af46eb1

Nonce

1,193,069,308

Timestamp

9/12/2017, 2:53:33 AM

Confirmations

4,550,718

Mined by

⛏️ P2SHAe8euNKGg2AZVSRyvrwCjkkPvQc1Lj4fiW

Merkle Root

766388d7b3fd971fe7e4e70ab3cc6eee2cbd2f1dde217fd5ceb53e8e9296511d

Transactions (3)

Coinbase0435b00d061843…ccdce1788525df

1 in → 1 out8.3400 XPM109 B

Ae8euNKG…c1Lj4fiW

932623bcf12414…6ace38e55474b9

1 in → 2 out4768.7900 XPM227 B

AYVBmLey…e5tVN1ar APh6iKe6…PS8AKMVZ

8fedaf09e9ddf9…4b839503c112ca

1 in → 2 out4131.0006 XPM226 B

ANT2eK4Z…BXaqvjpb AdQWz9jS…3LV6xQk4

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.

1.229 × 10⁹⁴(95-digit number)

12293699983508639427…60430679358019297279

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

1.229 × 10⁹⁴(95-digit number)

12293699983508639427…60430679358019297279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.229 × 10⁹⁴(95-digit number)

12293699983508639427…60430679358019297281

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

2.458 × 10⁹⁴(95-digit number)

24587399967017278855…20861358716038594559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.458 × 10⁹⁴(95-digit number)

24587399967017278855…20861358716038594561

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

4.917 × 10⁹⁴(95-digit number)

49174799934034557710…41722717432077189119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.917 × 10⁹⁴(95-digit number)

49174799934034557710…41722717432077189121

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

9.834 × 10⁹⁴(95-digit number)

98349599868069115420…83445434864154378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.834 × 10⁹⁴(95-digit number)

98349599868069115420…83445434864154378241

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

1.966 × 10⁹⁵(96-digit number)

19669919973613823084…66890869728308756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.966 × 10⁹⁵(96-digit number)

19669919973613823084…66890869728308756481

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

3.933 × 10⁹⁵(96-digit number)

39339839947227646168…33781739456617512959

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 #2,292,893

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