Block #206,967

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 3:47:23 AM · Difficulty 9.9018 · 6,602,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28be1398dbe3e1317ffa434ccd46b0d764f3a3dca8aaaa94a64b3191c9acee4d

View on Chainz ↗

Height

#206,967

Difficulty

9.901802

Transactions

Size

12.12 KB

Version

Bits

09e6dc77

Nonce

215,684

Timestamp

10/13/2013, 3:47:23 AM

Confirmations

6,602,184

Mined by

⛏️ P2SHANNQjLEpZ4WgsDvFZ5dNRmaLdVGddva1Pt

Merkle Root

57829ec773fd5b7761a25ff74b8e88cb6e36753e34c14b8bb693ae8b822aa8d8

Transactions (2)

Coinbase5c59bb07e75039…f71a00c636de05

1 in → 1 out10.3100 XPM109 B

ANNQjLEp…Gddva1Pt

0485f7e4c4fabd…a2b4235d847d41

82 in → 2 out77.0100 XPM11.93 KB

AVBgZjSd…KKtmPraK ARH6x196…JGnqgLDC

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.

6.856 × 10⁹²(93-digit number)

68560854156829979316…85222871107228344319

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

6.856 × 10⁹²(93-digit number)

68560854156829979316…85222871107228344319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.856 × 10⁹²(93-digit number)

68560854156829979316…85222871107228344321

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

1.371 × 10⁹³(94-digit number)

13712170831365995863…70445742214456688639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.371 × 10⁹³(94-digit number)

13712170831365995863…70445742214456688641

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

2.742 × 10⁹³(94-digit number)

27424341662731991726…40891484428913377279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.742 × 10⁹³(94-digit number)

27424341662731991726…40891484428913377281

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

5.484 × 10⁹³(94-digit number)

54848683325463983453…81782968857826754559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.484 × 10⁹³(94-digit number)

54848683325463983453…81782968857826754561

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

1.096 × 10⁹⁴(95-digit number)

10969736665092796690…63565937715653509119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.096 × 10⁹⁴(95-digit number)

10969736665092796690…63565937715653509121

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 #206,967

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