Block #271,243

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 12:20:54 PM · Difficulty 9.9518 · 6,538,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fdd679244d6cf8ccccbe8da86278bf92d57072c533b8303f6da0fc798dc4254

View on Chainz ↗

Height

#271,243

Difficulty

9.951768

Transactions

Size

759 B

Version

Bits

09f3a70c

Nonce

135,905

Timestamp

11/24/2013, 12:20:54 PM

Confirmations

6,538,673

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

26484147363304855a09d8751c08f98af900d8d4ec465178c858b853eece4531

Transactions (2)

Coinbased2bb9850704f49…653b4941631bc7

1 in → 2 out10.0900 XPM142 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

96f33861a0ea53…e46d8fda670a97

3 in → 2 out3.9568 XPM523 B

AZXA1nJz…vZgsKUSo AMWVTUQA…KAAUyEB8

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.

6.552 × 10¹⁰³(104-digit number)

65520381242311109223…39930230133720243199

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

6.552 × 10¹⁰³(104-digit number)

65520381242311109223…39930230133720243199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.552 × 10¹⁰³(104-digit number)

65520381242311109223…39930230133720243201

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

1.310 × 10¹⁰⁴(105-digit number)

13104076248462221844…79860460267440486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.310 × 10¹⁰⁴(105-digit number)

13104076248462221844…79860460267440486401

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

2.620 × 10¹⁰⁴(105-digit number)

26208152496924443689…59720920534880972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.620 × 10¹⁰⁴(105-digit number)

26208152496924443689…59720920534880972801

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

5.241 × 10¹⁰⁴(105-digit number)

52416304993848887378…19441841069761945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.241 × 10¹⁰⁴(105-digit number)

52416304993848887378…19441841069761945601

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

1.048 × 10¹⁰⁵(106-digit number)

10483260998769777475…38883682139523891199

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 #271,243

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