Block #2,762,092

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/23/2018, 8:34:04 PM · Difficulty 11.6550 · 4,036,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a0bc676f2fe51e43141d2eb081029ab93160ed11c4ebb57d3faf33326310322

View on Chainz ↗

Height

#2,762,092

Difficulty

11.655004

Transactions

Size

1.82 KB

Version

Bits

0ba7ae53

Nonce

118,926,650

Timestamp

7/23/2018, 8:34:04 PM

Confirmations

4,036,918

Mined by

⛏️ P2SHAK7dVHEFkHmnUmusffxzmcRVt2ZSvfVv7k

Merkle Root

8a2551ce55a5e55c254c9cb2c02a627eb76fa583658979592c39ca8ad9441fab

Transactions (5)

Coinbasea8a997cb8e863d…6b47f56df7bc26

1 in → 1 out7.3900 XPM110 B

AK7dVHEF…ZSvfVv7k

03e9e415bb5afb…c9be46e4aaf20b

2 in → 2 out14.7200 XPM304 B

AWAdNmTx…7LrP7LJM AQ7S9cWe…rDsLcCRa

52004b8efd57dd…48e96d4deb5bf4

5 in → 2 out35.6578 XPM680 B

AYnwdJT7…p81CDE6j AWp4iAg7…FUBLEm8x

86e60f2982a7f3…9df23bae1bd356

2 in → 2 out12.0000 XPM341 B

ATfqB6z9…uWgiRnGs AMCbCBhi…bevCqeNv

297495825a1966…268eea1556aa3e

2 in → 2 out12.0100 XPM342 B

AKD9LeNP…bQTn8mEf Ab3ocggh…Qe2u2zRP

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.

7.075 × 10⁹⁴(95-digit number)

70753563260371767887…43743716945492070399

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

7.075 × 10⁹⁴(95-digit number)

70753563260371767887…43743716945492070399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.075 × 10⁹⁴(95-digit number)

70753563260371767887…43743716945492070401

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

1.415 × 10⁹⁵(96-digit number)

14150712652074353577…87487433890984140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.415 × 10⁹⁵(96-digit number)

14150712652074353577…87487433890984140801

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

2.830 × 10⁹⁵(96-digit number)

28301425304148707155…74974867781968281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.830 × 10⁹⁵(96-digit number)

28301425304148707155…74974867781968281601

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

5.660 × 10⁹⁵(96-digit number)

56602850608297414310…49949735563936563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.660 × 10⁹⁵(96-digit number)

56602850608297414310…49949735563936563201

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

1.132 × 10⁹⁶(97-digit number)

11320570121659482862…99899471127873126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.132 × 10⁹⁶(97-digit number)

11320570121659482862…99899471127873126401

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

2.264 × 10⁹⁶(97-digit number)

22641140243318965724…99798942255746252799

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