Block #221,408

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 1:47:07 PM · Difficulty 9.9387 · 6,587,741 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b56753adc092a4befcb1f36a2222d797dc316641c19343b6b5a8890ad34fd72e

View on Chainz ↗

Height

#221,408

Difficulty

9.938686

Transactions

Size

5.33 KB

Version

Bits

09f04db4

Nonce

6,416

Timestamp

10/21/2013, 1:47:07 PM

Confirmations

6,587,741

Mined by

⛏️ P2SHAHUkw94B3RKU5ALGHAcaKgsxynZwfRe7XR

Merkle Root

89fed61079f35ed4c6d03118163afc2104567993b3ed0660595b921db57fcece

Transactions (3)

Coinbase6705d7bfdc5893…fe1413b44ff850

1 in → 1 out10.2000 XPM109 B

AHUkw94B…ZwfRe7XR

a42cf3640cfa4a…046025f47db9af

32 in → 2 out1001.7477 XPM4.70 KB

AQU2PuBk…c8ZUcmc4 AUZBmQ4s…czuQc5eB

83a40e20774726…235b7d235f1aca

2 in → 6 out20.2500 XPM441 B

APYq627z…f4sQNhSZ ATn5gfzL…UWGXwTUs ANVVnfSX…hQNURhur AbuU1HhS…JPwsJEbB ARTJCDz1…oJ6Hi1d9

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.

3.620 × 10⁹⁵(96-digit number)

36202901414825425262…30583235095639263999

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

3.620 × 10⁹⁵(96-digit number)

36202901414825425262…30583235095639263999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.620 × 10⁹⁵(96-digit number)

36202901414825425262…30583235095639264001

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

7.240 × 10⁹⁵(96-digit number)

72405802829650850525…61166470191278527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.240 × 10⁹⁵(96-digit number)

72405802829650850525…61166470191278528001

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

1.448 × 10⁹⁶(97-digit number)

14481160565930170105…22332940382557055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.448 × 10⁹⁶(97-digit number)

14481160565930170105…22332940382557056001

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

2.896 × 10⁹⁶(97-digit number)

28962321131860340210…44665880765114111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.896 × 10⁹⁶(97-digit number)

28962321131860340210…44665880765114112001

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

5.792 × 10⁹⁶(97-digit number)

57924642263720680420…89331761530228223999

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 #221,408

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