Block #206,384

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 6:41:01 PM · Difficulty 9.9011 · 6,600,422 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

feed5c04b79b103789752bdf82b23f3cd7b70464d7c50ae9f7562d9b1dfe3b87

View on Chainz ↗

Height

#206,384

Difficulty

9.901050

Transactions

Size

949 B

Version

Bits

09e6ab3a

Nonce

3,536

Timestamp

10/12/2013, 6:41:01 PM

Confirmations

6,600,422

Mined by

⛏️ P2SHAXtUHczob3NNdpiGvxAE1JUJfgKe72YFw4

Merkle Root

d2e3e60ba52fdf9af517d1ea07cca71aa4e440f8dc66fcbd8fe52c60ce0a6707

Transactions (3)

Coinbasee58218b3e04841…0e48b6266b415f

1 in → 1 out10.2100 XPM110 B

AXtUHczo…Ke72YFw4

73f1eec8fb4044…47024db51fe4e4

2 in → 2 out20.3800 XPM373 B

AaX7PyUr…4cU4LWea ASuoUi24…FwBoFbxd

1a755deaf045a3…4c8b6fc7a83dd3

2 in → 2 out3.2900 XPM375 B

AScnrDPe…RdJRL7PT AY2UULAv…hPvbNg1w

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.

2.614 × 10⁹⁶(97-digit number)

26149922368495744825…11758634019525584879

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

2.614 × 10⁹⁶(97-digit number)

26149922368495744825…11758634019525584879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.614 × 10⁹⁶(97-digit number)

26149922368495744825…11758634019525584881

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

5.229 × 10⁹⁶(97-digit number)

52299844736991489650…23517268039051169759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.229 × 10⁹⁶(97-digit number)

52299844736991489650…23517268039051169761

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

1.045 × 10⁹⁷(98-digit number)

10459968947398297930…47034536078102339519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.045 × 10⁹⁷(98-digit number)

10459968947398297930…47034536078102339521

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

2.091 × 10⁹⁷(98-digit number)

20919937894796595860…94069072156204679039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.091 × 10⁹⁷(98-digit number)

20919937894796595860…94069072156204679041

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

4.183 × 10⁹⁷(98-digit number)

41839875789593191720…88138144312409358079

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 #206,384

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