Block #252,283

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 11:46:10 AM · Difficulty 9.9710 · 6,556,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ef4b39745f9815520eea6e3b6ecafba2935a33ead27216d5d9c3939e7208d26

View on Chainz ↗

Height

#252,283

Difficulty

9.971024

Transactions

Size

5.40 KB

Version

Bits

09f89500

Nonce

37,734

Timestamp

11/9/2013, 11:46:10 AM

Confirmations

6,556,736

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

9f50ee208a547af0556a6be8b03ae85885648d03f90f57ae3ea562c272ce3c5c

Transactions (3)

Coinbase2f53316b2c6f24…cf1557db3e245e

1 in → 2 out10.1000 XPM140 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

1cb8b577fce2cb…fc5381d12e47a9

2 in → 2 out61.1781 XPM375 B

AYmzdtJB…hiasyn2t AZ2RKcaG…w7SE65kY

3419a493cd7684…044c0b747b330d

33 in → 1 out4.1444 XPM4.81 KB

AYyQfxqf…T6UhSNqH

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.

2.415 × 10⁹⁶(97-digit number)

24150956492393133674…43077252636550401919

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

2.415 × 10⁹⁶(97-digit number)

24150956492393133674…43077252636550401919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.415 × 10⁹⁶(97-digit number)

24150956492393133674…43077252636550401921

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

4.830 × 10⁹⁶(97-digit number)

48301912984786267349…86154505273100803839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.830 × 10⁹⁶(97-digit number)

48301912984786267349…86154505273100803841

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

9.660 × 10⁹⁶(97-digit number)

96603825969572534698…72309010546201607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.660 × 10⁹⁶(97-digit number)

96603825969572534698…72309010546201607681

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

1.932 × 10⁹⁷(98-digit number)

19320765193914506939…44618021092403215359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.932 × 10⁹⁷(98-digit number)

19320765193914506939…44618021092403215361

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

3.864 × 10⁹⁷(98-digit number)

38641530387829013879…89236042184806430719

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 #252,283

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