Block #2,239,268

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/6/2017, 8:39:53 AM · Difficulty 10.9464 · 4,604,319 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a6966ee907294d4c92dac5dfdd4983962079e5f010d74e9ac74aa4a3d27f677

View on Chainz ↗

Height

#2,239,268

Difficulty

10.946354

Transactions

Size

582 B

Version

Bits

0af24444

Nonce

362,846,903

Timestamp

8/6/2017, 8:39:53 AM

Confirmations

4,604,319

Mined by

⛏️ P2SHAN9XUKJqq8FEEwLUVZQpqdrUy2Wm8wDQwV

Merkle Root

15375a003a079f08884017e7607e36b17cd7d10686d35cad53fab9a199b9560e

Transactions (3)

Coinbaseaecddb5430cea0…5a08e4177a2719

1 in → 1 out8.3500 XPM109 B

AN9XUKJq…Wm8wDQwV

6d54ef7f62486e…8812680c86c84e

1 in → 2 out8.3200 XPM193 B

AHTJyYeE…SyxHXkV7 ARuxmsMD…3hLKHBGJ

cf872bd4ae6dca…ba821a81cfa321

1 in → 2 out8.3200 XPM191 B

Ach8fSJX…WMvHR7M2 AHbyumek…ry7WXVsp

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.

5.622 × 10⁹²(93-digit number)

56224868758422155610…80473149337844312959

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

5.622 × 10⁹²(93-digit number)

56224868758422155610…80473149337844312959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.622 × 10⁹²(93-digit number)

56224868758422155610…80473149337844312961

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

1.124 × 10⁹³(94-digit number)

11244973751684431122…60946298675688625919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.124 × 10⁹³(94-digit number)

11244973751684431122…60946298675688625921

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

2.248 × 10⁹³(94-digit number)

22489947503368862244…21892597351377251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.248 × 10⁹³(94-digit number)

22489947503368862244…21892597351377251841

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

4.497 × 10⁹³(94-digit number)

44979895006737724488…43785194702754503679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.497 × 10⁹³(94-digit number)

44979895006737724488…43785194702754503681

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

8.995 × 10⁹³(94-digit number)

89959790013475448976…87570389405509007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.995 × 10⁹³(94-digit number)

89959790013475448976…87570389405509007361

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

1.799 × 10⁹⁴(95-digit number)

17991958002695089795…75140778811018014719

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 #2,239,268

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