Block #268,511

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 5:13:19 AM · Difficulty 9.9569 · 6,541,342 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c47f5aa7ca8d3c27f15ec1d5c582183598443c8516f261f69bf85900588e02b

View on Chainz ↗

Height

#268,511

Difficulty

9.956870

Transactions

Size

7.39 KB

Version

Bits

09f4f576

Nonce

5,501

Timestamp

11/22/2013, 5:13:19 AM

Confirmations

6,541,342

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

2bb9a5997e5081acb939d41f50fc7d3fe650b9db5a228f6b2775b3a2762415fb

Transactions (3)

Coinbase442ae37f311f00…76e9dc5feaf5d8

1 in → 2 out10.1554 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

4f11e89a7b92c8…78991db2778104

22 in → 1 out364.1200 XPM2.49 KB

AZEZiNXo…kWUj7oE6

f58495124d3820…d264f52d000a45

32 in → 1 out2.4000 XPM4.67 KB

AX3gi1Mo…4v25skFX

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.

2.760 × 10¹⁰³(104-digit number)

27606817337059308893…41291558375479634239

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

2.760 × 10¹⁰³(104-digit number)

27606817337059308893…41291558375479634239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.760 × 10¹⁰³(104-digit number)

27606817337059308893…41291558375479634241

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

5.521 × 10¹⁰³(104-digit number)

55213634674118617787…82583116750959268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.521 × 10¹⁰³(104-digit number)

55213634674118617787…82583116750959268481

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

1.104 × 10¹⁰⁴(105-digit number)

11042726934823723557…65166233501918536959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.104 × 10¹⁰⁴(105-digit number)

11042726934823723557…65166233501918536961

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

2.208 × 10¹⁰⁴(105-digit number)

22085453869647447115…30332467003837073919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.208 × 10¹⁰⁴(105-digit number)

22085453869647447115…30332467003837073921

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

4.417 × 10¹⁰⁴(105-digit number)

44170907739294894230…60664934007674147839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #268,511

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