Block #2,803,291

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/21/2018, 8:54:51 AM · Difficulty 11.6658 · 4,039,971 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9a99e8c608ca92c6b24fbf43f2bbc9c1c09b8dfdac968a875cd8da31fb62139

View on Chainz ↗

Height

#2,803,291

Difficulty

11.665843

Transactions

Size

879 B

Version

Bits

0baa74b0

Nonce

2,064,403,446

Timestamp

8/21/2018, 8:54:51 AM

Confirmations

4,039,971

Mined by

⛏️ P2SHAaEZCN53nPeipveeayK9VhYYSAoxyrgCyD

Merkle Root

0f488b4a7e4f8f3d4f60d5dfe5890bd0a44263796f3b39e93d57de070818da89

Transactions (4)

Coinbase27a9a07f04cc48…42f6bfe7312225

1 in → 1 out7.3700 XPM110 B

AaEZCN53…oxyrgCyD

be2c0e03b0d97d…9c9711f9478e07

1 in → 2 out4.6600 XPM227 B

AeW579ge…zHL6jv8g AJk76m7n…5c12ta2b

5c82a3a09c06a3…624874ee0f9a99

1 in → 2 out2.7641 XPM225 B

AV3JM4zu…4Yqk98pg AcgtSNxU…6ERZZjkk

ac694b3269d733…19215c1aded00d

1 in → 2 out0.9463 XPM227 B

AQMVnZwY…EV6hUzKa Aatwb5m5…CpUGXNMa

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.

1.273 × 10⁹⁵(96-digit number)

12736826221365242699…47960841586840583679

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

1.273 × 10⁹⁵(96-digit number)

12736826221365242699…47960841586840583679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.273 × 10⁹⁵(96-digit number)

12736826221365242699…47960841586840583681

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

2.547 × 10⁹⁵(96-digit number)

25473652442730485399…95921683173681167359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.547 × 10⁹⁵(96-digit number)

25473652442730485399…95921683173681167361

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

5.094 × 10⁹⁵(96-digit number)

50947304885460970799…91843366347362334719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.094 × 10⁹⁵(96-digit number)

50947304885460970799…91843366347362334721

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

1.018 × 10⁹⁶(97-digit number)

10189460977092194159…83686732694724669439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.018 × 10⁹⁶(97-digit number)

10189460977092194159…83686732694724669441

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

2.037 × 10⁹⁶(97-digit number)

20378921954184388319…67373465389449338879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.037 × 10⁹⁶(97-digit number)

20378921954184388319…67373465389449338881

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

4.075 × 10⁹⁶(97-digit number)

40757843908368776639…34746930778898677759

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 #2,803,291

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