Block #209,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 3:19:33 PM · Difficulty 9.9098 · 6,600,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4c61f0b00e9d24c903b1386b6c46853fb4d45ad5a5ebaa02ff17c4d5da6b100

View on Chainz ↗

Height

#209,522

Difficulty

9.909800

Transactions

Size

1.04 KB

Version

Bits

09e8e8a2

Nonce

11,630

Timestamp

10/14/2013, 3:19:33 PM

Confirmations

6,600,046

Mined by

⛏️ P2SHAJHDuUknZ4xP6FCti3qBa2FdbyqceWDJrc

Merkle Root

1e02932fadd29e4c08203b3fe9479c1e86704d35a81a3c87020d81b379460369

Transactions (4)

Coinbase014ae63074f6bd…b1fe4a20e09d2a

1 in → 1 out10.2000 XPM109 B

AJHDuUkn…qceWDJrc

fcdc93354815ad…5b0f0d5cbc3087

1 in → 2 out10.1900 XPM192 B

ATDh6dQJ…Y3bZUXRr AaMRUFMG…S11BNFrC

b6dac82e736d3e…a6120afab9b8a1

3 in → 2 out10.4600 XPM489 B

AX73dxCy…fMsyAg1C AQAvQSWZ…C9mFkvux

23ae3b02931b53…bfd9c7f48efefc

1 in → 1 out5.0900 XPM191 B

AeguK5Ai…CLUqoF9q

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.

2.457 × 10⁸⁷(88-digit number)

24573361628252338134…49853700870816256959

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

2.457 × 10⁸⁷(88-digit number)

24573361628252338134…49853700870816256959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.457 × 10⁸⁷(88-digit number)

24573361628252338134…49853700870816256961

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

4.914 × 10⁸⁷(88-digit number)

49146723256504676269…99707401741632513919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.914 × 10⁸⁷(88-digit number)

49146723256504676269…99707401741632513921

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

9.829 × 10⁸⁷(88-digit number)

98293446513009352539…99414803483265027839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.829 × 10⁸⁷(88-digit number)

98293446513009352539…99414803483265027841

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

1.965 × 10⁸⁸(89-digit number)

19658689302601870507…98829606966530055679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.965 × 10⁸⁸(89-digit number)

19658689302601870507…98829606966530055681

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

3.931 × 10⁸⁸(89-digit number)

39317378605203741015…97659213933060111359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.931 × 10⁸⁸(89-digit number)

39317378605203741015…97659213933060111361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #209,522

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