Block #2,793,089

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/14/2018, 3:27:49 AM · Difficulty 11.6786 · 4,049,078 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf5639644bc39d04e45f11127005e5dac1a66160928ac55df9080d5b89804ca3

View on Chainz ↗

Height

#2,793,089

Difficulty

11.678640

Transactions

Size

1.86 KB

Version

Bits

0badbb5e

Nonce

1,404,024,891

Timestamp

8/14/2018, 3:27:49 AM

Confirmations

4,049,078

Mined by

⛏️ P2SHAGnNJE4HPLPHuEb7dLuTJRqcmcm6q4cZva

Merkle Root

0e0bf8f1e377d5ad84d842e95f24ee2ebd875df8e0290b4ca7b5b82caaed24cf

Transactions (2)

Coinbaseade4ca31d1cbdf…7ce59860668001

1 in → 1 out7.3500 XPM110 B

AGnNJE4H…m6q4cZva

0deb0e9587605c…27a20507a48b31

11 in → 2 out9466.2762 XPM1.67 KB

AKpc4vNR…MWZMpqvb AT7R24XJ…gwCnPYp5

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.

1.382 × 10⁹³(94-digit number)

13827680714465841023…15621504248993056109

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

1.382 × 10⁹³(94-digit number)

13827680714465841023…15621504248993056109

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.382 × 10⁹³(94-digit number)

13827680714465841023…15621504248993056111

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

2.765 × 10⁹³(94-digit number)

27655361428931682047…31243008497986112219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.765 × 10⁹³(94-digit number)

27655361428931682047…31243008497986112221

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

5.531 × 10⁹³(94-digit number)

55310722857863364095…62486016995972224439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.531 × 10⁹³(94-digit number)

55310722857863364095…62486016995972224441

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

1.106 × 10⁹⁴(95-digit number)

11062144571572672819…24972033991944448879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.106 × 10⁹⁴(95-digit number)

11062144571572672819…24972033991944448881

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

2.212 × 10⁹⁴(95-digit number)

22124289143145345638…49944067983888897759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.212 × 10⁹⁴(95-digit number)

22124289143145345638…49944067983888897761

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

4.424 × 10⁹⁴(95-digit number)

44248578286290691276…99888135967777795519

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 #2,793,089

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