Block #2,733,149

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/4/2018, 12:07:25 AM · Difficulty 11.6286 · 4,109,516 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

819b9fbab763bb197bf2b5da9135d9099308235a11ff8727a6afd5ecd9aed9f9

View on Chainz ↗

Height

#2,733,149

Difficulty

11.628601

Transactions

Size

1.31 KB

Version

Bits

0ba0ebfb

Nonce

353,234,468

Timestamp

7/4/2018, 12:07:25 AM

Confirmations

4,109,516

Mined by

⛏️ P2SHAXVJ6i7WhsezgyzHTE17gm17qbuqMH8af8

Merkle Root

a0d0a0e56653564e91a36aefb6dba67ed34c77e61e32c43a7c02e64bf3ec2ab4

Transactions (4)

Coinbasef949448df384c6…6fe0815a0f6bfe

1 in → 1 out7.4100 XPM110 B

AXVJ6i7W…uqMH8af8

e24b772073e694…77c46748ec6db4

2 in → 2 out14.7500 XPM308 B

AKnggQhu…ocBg7cEn ASYvjRCx…KpswhHRf

41cbebf9f8b811…36f7c0bf32418e

2 in → 2 out12.1300 XPM341 B

AK7M9NX8…jF3KHGZj AbgAFYLg…mepR97Tq

3ba33546b62cf4…aa61bf38e9336d

3 in → 2 out10.2600 XPM489 B

APVKWthF…PMMxwRoz ANo6cgjE…LktTCVRK

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.

2.215 × 10⁹⁸(99-digit number)

22154278923705584816…01369531008181534719

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

2.215 × 10⁹⁸(99-digit number)

22154278923705584816…01369531008181534719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.215 × 10⁹⁸(99-digit number)

22154278923705584816…01369531008181534721

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

4.430 × 10⁹⁸(99-digit number)

44308557847411169633…02739062016363069439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.430 × 10⁹⁸(99-digit number)

44308557847411169633…02739062016363069441

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

8.861 × 10⁹⁸(99-digit number)

88617115694822339266…05478124032726138879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.861 × 10⁹⁸(99-digit number)

88617115694822339266…05478124032726138881

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

1.772 × 10⁹⁹(100-digit number)

17723423138964467853…10956248065452277759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.772 × 10⁹⁹(100-digit number)

17723423138964467853…10956248065452277761

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

3.544 × 10⁹⁹(100-digit number)

35446846277928935706…21912496130904555519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.544 × 10⁹⁹(100-digit number)

35446846277928935706…21912496130904555521

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

7.089 × 10⁹⁹(100-digit number)

70893692555857871412…43824992261809111039

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 #2,733,149

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