Block #2,184,364

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/29/2017, 8:10:45 AM · Difficulty 10.9429 · 4,647,388 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f297b26ea69d6199de065c0fc80886b270376857e4abc15581b1ff60441fc05b

View on Chainz ↗

Height

#2,184,364

Difficulty

10.942894

Transactions

Size

653 B

Version

Bits

0af16186

Nonce

1,351,795,479

Timestamp

6/29/2017, 8:10:45 AM

Confirmations

4,647,388

Mined by

⛏️ P2SHAeAq2J29GCuMsBozySZh6rkAjAUXTe18Up

Merkle Root

def6b5c3ad797305973e4d05b5dc00fe57994e69744c5257eacaa2b0cad3e166

Transactions (3)

Coinbased0bc24b9f2cff9…8ef63d4080591c

1 in → 1 out8.3600 XPM110 B

AeAq2J29…UXTe18Up

35f0371434860e…95c2e6846ea502

1 in → 2 out2969.9900 XPM226 B

AammHJuN…yaRcHuV7 ARmaUDVL…4bFUtL75

7d478a6532a7a6…01d349b1a0f135

1 in → 2 out989.9900 XPM227 B

AYVBmLey…e5tVN1ar ASbuAy6v…f51Ffstb

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.

1.120 × 10⁹⁵(96-digit number)

11200929332638466474…17248557571131073279

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

1.120 × 10⁹⁵(96-digit number)

11200929332638466474…17248557571131073279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.120 × 10⁹⁵(96-digit number)

11200929332638466474…17248557571131073281

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

2.240 × 10⁹⁵(96-digit number)

22401858665276932949…34497115142262146559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.240 × 10⁹⁵(96-digit number)

22401858665276932949…34497115142262146561

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

4.480 × 10⁹⁵(96-digit number)

44803717330553865898…68994230284524293119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.480 × 10⁹⁵(96-digit number)

44803717330553865898…68994230284524293121

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

8.960 × 10⁹⁵(96-digit number)

89607434661107731797…37988460569048586239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.960 × 10⁹⁵(96-digit number)

89607434661107731797…37988460569048586241

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

1.792 × 10⁹⁶(97-digit number)

17921486932221546359…75976921138097172479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.792 × 10⁹⁶(97-digit number)

17921486932221546359…75976921138097172481

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

3.584 × 10⁹⁶(97-digit number)

35842973864443092719…51953842276194344959

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 #2,184,364

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