Block #252,411

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 1:34:39 PM · Difficulty 9.9711 · 6,551,223 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ffd80e6bdaa90b39b43791d98dd67615c4c79fe02031d257b626382696de1c6

View on Chainz ↗

Height

#252,411

Difficulty

9.971124

Transactions

Size

2.20 KB

Version

Bits

09f89b97

Nonce

41,738

Timestamp

11/9/2013, 1:34:39 PM

Confirmations

6,551,223

Mined by

⛏️ aR~9AeLaP1NXtHT5Dok2uN5HSW1Y29SJ53Q2G7

Merkle Root

f3b60edc77149692f31dfb4816ae7c60aa13d6102e485b69099ea9f3adb7a406

Transactions (2)

Coinbase849d2524528a63…cd5fd18c1842e8

1 in → 55 out10.0200 XPM1.89 KB

AeLaP1NX…SJ53Q2G7 AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AHkgKuuD…TkWqWiw1 AJzWx2VD…j4ZSMit5

69a951c298b01c…fe5ed6832b8499

1 in → 2 out5.8825 XPM227 B

AUHkbont…3T2G3Jn2 AZSEnAzR…t3o7JHac

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.

3.678 × 10⁹⁶(97-digit number)

36786100586082590633…89367357059043491399

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

3.678 × 10⁹⁶(97-digit number)

36786100586082590633…89367357059043491399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.678 × 10⁹⁶(97-digit number)

36786100586082590633…89367357059043491401

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

7.357 × 10⁹⁶(97-digit number)

73572201172165181266…78734714118086982799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.357 × 10⁹⁶(97-digit number)

73572201172165181266…78734714118086982801

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

1.471 × 10⁹⁷(98-digit number)

14714440234433036253…57469428236173965599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.471 × 10⁹⁷(98-digit number)

14714440234433036253…57469428236173965601

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

2.942 × 10⁹⁷(98-digit number)

29428880468866072506…14938856472347931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.942 × 10⁹⁷(98-digit number)

29428880468866072506…14938856472347931201

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

5.885 × 10⁹⁷(98-digit number)

58857760937732145013…29877712944695862399

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