Block #2,784,400

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/8/2018, 5:17:20 AM · Difficulty 11.6681 · 4,054,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

580552ca39e3a6388b87b9cc8fde56c04aab4e9a6095d6d77caaed6dc475cd67

View on Chainz ↗

Height

#2,784,400

Difficulty

11.668103

Transactions

Size

1.71 KB

Version

Bits

0bab08c7

Nonce

7,068,651

Timestamp

8/8/2018, 5:17:20 AM

Confirmations

4,054,918

Mined by

⛏️ P2SHAXmvAn2GRb39GguPRBEmAvNRnN8MdMu6ut

Merkle Root

eee562ea6ca1b93c7b54778a6f00644816801b8bab21f5f93486b7bb82f866d3

Transactions (2)

Coinbase1f43de683201d6…e76c9eefdd2bea

1 in → 1 out7.3500 XPM110 B

AXmvAn2G…8MdMu6ut

e864308140f95e…2a78c6804cc91a

10 in → 2 out45.9929 XPM1.52 KB

AZdgBzKe…nxAM35Hv AXiP3Tpq…bJCCTNCr

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.

3.187 × 10⁹⁶(97-digit number)

31873173420905397026…52335016969448857599

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

3.187 × 10⁹⁶(97-digit number)

31873173420905397026…52335016969448857599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.187 × 10⁹⁶(97-digit number)

31873173420905397026…52335016969448857601

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

6.374 × 10⁹⁶(97-digit number)

63746346841810794052…04670033938897715199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.374 × 10⁹⁶(97-digit number)

63746346841810794052…04670033938897715201

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

1.274 × 10⁹⁷(98-digit number)

12749269368362158810…09340067877795430399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.274 × 10⁹⁷(98-digit number)

12749269368362158810…09340067877795430401

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

2.549 × 10⁹⁷(98-digit number)

25498538736724317620…18680135755590860799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.549 × 10⁹⁷(98-digit number)

25498538736724317620…18680135755590860801

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

5.099 × 10⁹⁷(98-digit number)

50997077473448635241…37360271511181721599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.099 × 10⁹⁷(98-digit number)

50997077473448635241…37360271511181721601

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

1.019 × 10⁹⁸(99-digit number)

10199415494689727048…74720543022363443199

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 #2,784,400

Cookie Preferences