Block #243,342

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 6:14:55 AM · Difficulty 9.9613 · 6,563,169 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

19fccd53c19d0cc7bae00a81e2a0ed12ab3db49d7cbf99526c6a167da9d7f017

View on Chainz ↗

Height

#243,342

Difficulty

9.961271

Transactions

Size

4.31 KB

Version

Bits

09f615db

Nonce

24,180

Timestamp

11/4/2013, 6:14:55 AM

Confirmations

6,563,169

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

d1367da4fb5de0b3570ea1dde624104fe810734144e8da13af9ef2f75a94b1cb

Transactions (3)

Coinbase2bf197a0288da5…9cc82d885aa2ab

1 in → 2 out10.1100 XPM137 B

ARmAMwyu…P7Kn74ZT AKNbfPoc…jfkpwAyL

335c0bfa12df74…8a3b98f9ba97a2

3 in → 2 out300.1500 XPM489 B

AYjSbdV3…7Z9wbYkZ AQh5PYkW…KncvxhcL

ee5f44e0b31285…3b16b0e76095d0

32 in → 1 out324.2283 XPM3.61 KB

AQjAX9Vk…hTks6kYK

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.

5.441 × 10⁹⁹(100-digit number)

54413950113037411769…13862308491730766079

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

5.441 × 10⁹⁹(100-digit number)

54413950113037411769…13862308491730766079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.441 × 10⁹⁹(100-digit number)

54413950113037411769…13862308491730766081

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

1.088 × 10¹⁰⁰(101-digit number)

10882790022607482353…27724616983461532159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.088 × 10¹⁰⁰(101-digit number)

10882790022607482353…27724616983461532161

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

2.176 × 10¹⁰⁰(101-digit number)

21765580045214964707…55449233966923064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.176 × 10¹⁰⁰(101-digit number)

21765580045214964707…55449233966923064321

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

4.353 × 10¹⁰⁰(101-digit number)

43531160090429929415…10898467933846128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.353 × 10¹⁰⁰(101-digit number)

43531160090429929415…10898467933846128641

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

8.706 × 10¹⁰⁰(101-digit number)

87062320180859858830…21796935867692257279

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 #243,342

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