Block #205,532

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 5:16:01 AM · Difficulty 9.9000 · 6,598,135 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6100eabe1ada14daffd6e718020aa20eb6c5acdf0d0025c7f11f1a2b14db51e

View on Chainz ↗

Height

#205,532

Difficulty

9.900028

Transactions

Size

1.00 KB

Version

Bits

09e6683d

Nonce

88,720

Timestamp

10/12/2013, 5:16:01 AM

Confirmations

6,598,135

Mined by

⛏️ P2SHAcT2fEb5AHzdW6GsysVbJnPJoBt73QEQRo

Merkle Root

6c26a5575d86e6275ac400cd263bda05ce1b728414dcfc5ddbb985e6b624e8be

Transactions (3)

Coinbase04f9ec2484eeac…052c4153a9d6ee

1 in → 1 out10.2100 XPM109 B

AcT2fEb5…t73QEQRo

3df1398cfc64cf…7faff714020737

1 in → 2 out10.1900 XPM191 B

AZ2SDqri…cBGkUMfR AFz9fXym…wh4UqpkL

161c683148ef9f…11aba9cef69798

4 in → 2 out11.1100 XPM637 B

APqRQzyF…SHEK77Yc AFz9fXym…wh4UqpkL

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.

1.277 × 10⁸⁹(90-digit number)

12774206815050038149…46292818867176680519

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

1.277 × 10⁸⁹(90-digit number)

12774206815050038149…46292818867176680519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.277 × 10⁸⁹(90-digit number)

12774206815050038149…46292818867176680521

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

2.554 × 10⁸⁹(90-digit number)

25548413630100076298…92585637734353361039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.554 × 10⁸⁹(90-digit number)

25548413630100076298…92585637734353361041

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

5.109 × 10⁸⁹(90-digit number)

51096827260200152597…85171275468706722079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.109 × 10⁸⁹(90-digit number)

51096827260200152597…85171275468706722081

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

1.021 × 10⁹⁰(91-digit number)

10219365452040030519…70342550937413444159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.021 × 10⁹⁰(91-digit number)

10219365452040030519…70342550937413444161

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

2.043 × 10⁹⁰(91-digit number)

20438730904080061038…40685101874826888319

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