Block #209,563

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 3:49:09 PM · Difficulty 9.9100 · 6,597,788 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04a5d6501e55e0cf7ffd6399f50a538a1d39abfc8d083f6becc7b9a7f9d846ce

View on Chainz ↗

Height

#209,563

Difficulty

9.909994

Transactions

Size

1.77 KB

Version

Bits

09e8f55e

Nonce

3,463

Timestamp

10/14/2013, 3:49:09 PM

Confirmations

6,597,788

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

1329c58e7e3a3db709c323f5f5897ba37489de93acefc0e4892084de206e1d9f

Transactions (4)

Coinbase636b954395196f…794919de65a903

1 in → 1 out10.2152 XPM110 B

AbuU1HhS…JPwsJEbB

87806d7cb76026…063bd01e376e38

1 in → 2 out10.1800 XPM192 B

AQAvQSWZ…C9mFkvux AGjjFwqW…Jke8YS7i

e7df626785ea77…aa2d8ebc931169

7 in → 1 out21.4400 XPM1.05 KB

AQrHZqm1…4FnEdPi6

83eb32821d9305…c15427eef3bbda

2 in → 1 out2.0700 XPM342 B

ATaF1JyB…Lo75UW58

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.

2.723 × 10⁹⁰(91-digit number)

27232801379885191947…35899990064535018459

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

2.723 × 10⁹⁰(91-digit number)

27232801379885191947…35899990064535018459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.723 × 10⁹⁰(91-digit number)

27232801379885191947…35899990064535018461

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

5.446 × 10⁹⁰(91-digit number)

54465602759770383894…71799980129070036919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.446 × 10⁹⁰(91-digit number)

54465602759770383894…71799980129070036921

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

1.089 × 10⁹¹(92-digit number)

10893120551954076778…43599960258140073839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.089 × 10⁹¹(92-digit number)

10893120551954076778…43599960258140073841

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

2.178 × 10⁹¹(92-digit number)

21786241103908153557…87199920516280147679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.178 × 10⁹¹(92-digit number)

21786241103908153557…87199920516280147681

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

4.357 × 10⁹¹(92-digit number)

43572482207816307115…74399841032560295359

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 #209,563

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