Block #211,979

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 12:20:14 AM · Difficulty 9.9182 · 6,591,624 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4dd93e1632952f75fe4795031dffa6404f78ded50a42482f5b1f04c57ddad46

View on Chainz ↗

Height

#211,979

Difficulty

9.918162

Transactions

Size

1.72 KB

Version

Bits

09eb0ca5

Nonce

191,445

Timestamp

10/16/2013, 12:20:14 AM

Confirmations

6,591,624

Mined by

⛏️ P2SHARsxB1G4W7sQNfH57WppzJqinUmoBvdb8v

Merkle Root

35ae6340badae179f72cc5ea39347c09969ff5bef8de67a5ce54df13f153e315

Transactions (2)

Coinbase62c0b43a788361…b407385bbc73ad

1 in → 1 out10.1900 XPM109 B

ARsxB1G4…moBvdb8v

b5cc037adceece…a71942355d084f

10 in → 2 out49.8100 XPM1.52 KB

AHvZubsu…6NRQXYTt AJM6aWAG…whFENXCA

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.

9.038 × 10⁹⁴(95-digit number)

90382354044066458119…00763311360938395139

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

9.038 × 10⁹⁴(95-digit number)

90382354044066458119…00763311360938395139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.038 × 10⁹⁴(95-digit number)

90382354044066458119…00763311360938395141

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

1.807 × 10⁹⁵(96-digit number)

18076470808813291623…01526622721876790279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.807 × 10⁹⁵(96-digit number)

18076470808813291623…01526622721876790281

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

3.615 × 10⁹⁵(96-digit number)

36152941617626583247…03053245443753580559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.615 × 10⁹⁵(96-digit number)

36152941617626583247…03053245443753580561

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

7.230 × 10⁹⁵(96-digit number)

72305883235253166495…06106490887507161119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.230 × 10⁹⁵(96-digit number)

72305883235253166495…06106490887507161121

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

1.446 × 10⁹⁶(97-digit number)

14461176647050633299…12212981775014322239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.446 × 10⁹⁶(97-digit number)

14461176647050633299…12212981775014322241

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