Block #2,649,273

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 3:00:02 AM · Difficulty 11.7650 · 4,182,275 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30b5ec5743787b68b6134a30f98bf50af7d56d1b4ec64efe1ebd19ed1c2dba83

View on Chainz ↗

Height

#2,649,273

Difficulty

11.765026

Transactions

Size

1.43 KB

Version

Bits

0bc3d8c4

Nonce

1,485,104,647

Timestamp

5/5/2018, 3:00:02 AM

Confirmations

4,182,275

Mined by

⛏️ P2SHAbepJLBmZEXHi8uMWkYnb2QpcDVcSk9MeU

Merkle Root

e2ec6b465757a75a0c4968cf4d5d83872cb3defc3d51bf1623bf2427bdf45ed6

Transactions (2)

Coinbasee19183ffc240d4…0e154d6ec01ba8

1 in → 1 out7.2300 XPM109 B

AbepJLBm…VcSk9MeU

9ddab57bbbac69…3927eaff87fad8

8 in → 2 out76.5089 XPM1.23 KB

AXDznZG3…PDHnfomC AQHWijZe…tPphNvCB

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.

2.044 × 10⁹⁶(97-digit number)

20444470723652188930…51116341896720547839

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

2.044 × 10⁹⁶(97-digit number)

20444470723652188930…51116341896720547839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.044 × 10⁹⁶(97-digit number)

20444470723652188930…51116341896720547841

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

4.088 × 10⁹⁶(97-digit number)

40888941447304377861…02232683793441095679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.088 × 10⁹⁶(97-digit number)

40888941447304377861…02232683793441095681

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

8.177 × 10⁹⁶(97-digit number)

81777882894608755723…04465367586882191359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.177 × 10⁹⁶(97-digit number)

81777882894608755723…04465367586882191361

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

1.635 × 10⁹⁷(98-digit number)

16355576578921751144…08930735173764382719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.635 × 10⁹⁷(98-digit number)

16355576578921751144…08930735173764382721

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

3.271 × 10⁹⁷(98-digit number)

32711153157843502289…17861470347528765439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.271 × 10⁹⁷(98-digit number)

32711153157843502289…17861470347528765441

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

6.542 × 10⁹⁷(98-digit number)

65422306315687004578…35722940695057530879

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 #2,649,273

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