Block #206,431

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 7:19:42 PM · Difficulty 9.9012 · 6,599,712 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be8df1f4e4e8d4f3aa6f41bd8010c7750aae8c3b68c68c54a520e5b9ad1d37c5

View on Chainz ↗

Height

#206,431

Difficulty

9.901200

Transactions

Size

2.09 KB

Version

Bits

09e6b503

Nonce

215

Timestamp

10/12/2013, 7:19:42 PM

Confirmations

6,599,712

Mined by

⛏️ P2SHARbSaFzbS6EX5zX8FsqKk6UJD52ndScSSm

Merkle Root

0d1b6249384f945942a699f02c537188a63341ca3c5bcf6f7320c039c91373e2

Transactions (5)

Coinbasebc6ecfd0ff0e5e…091b75cc9f679b

1 in → 1 out10.2300 XPM109 B

ARbSaFzb…2ndScSSm

e1055ca2d269e4…4a0cbdbb0fe71f

2 in → 2 out129.9405 XPM372 B

AcpXLu7P…ueRdfg3W AGyxfVtk…yxpPuyZq

f254b22d748f8c…e745d61c40b4f9

4 in → 2 out312.9754 XPM672 B

ARdqb1Rr…zbZGqjx2 AVYahico…oryG9wWS

1e6ac94961ed2e…01e6d5b9859ac2

3 in → 2 out30.5800 XPM521 B

AQt7xHtg…AXmNFrUW AQNrevBm…LNV5kY9b

07683c82eb54b4…7348600c365f76

2 in → 2 out13.0114 XPM374 B

AHYHSv47…pc3YeakF AHyHEeYQ…XuELsExj

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.

3.278 × 10⁹⁰(91-digit number)

32787341603836522648…86768307518967506559

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

3.278 × 10⁹⁰(91-digit number)

32787341603836522648…86768307518967506559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.278 × 10⁹⁰(91-digit number)

32787341603836522648…86768307518967506561

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

6.557 × 10⁹⁰(91-digit number)

65574683207673045297…73536615037935013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.557 × 10⁹⁰(91-digit number)

65574683207673045297…73536615037935013121

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

1.311 × 10⁹¹(92-digit number)

13114936641534609059…47073230075870026239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.311 × 10⁹¹(92-digit number)

13114936641534609059…47073230075870026241

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

2.622 × 10⁹¹(92-digit number)

26229873283069218119…94146460151740052479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.622 × 10⁹¹(92-digit number)

26229873283069218119…94146460151740052481

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

5.245 × 10⁹¹(92-digit number)

52459746566138436238…88292920303480104959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.245 × 10⁹¹(92-digit number)

52459746566138436238…88292920303480104961

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