Home/Chain Registry/Block #201,401

Block #201,401

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 3:18:07 PM · Difficulty 9.8912 · 6,593,104 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af820bb7bea50637cbf84d7ff5a8c6a44fc759e40ac6609f9c79183fb8e0b518

View on Chainz ↗

Height

#201,401

Difficulty

9.891230

Transactions

Size

1.13 KB

Version

Bits

09e4279f

Nonce

53,745

Timestamp

10/9/2013, 3:18:07 PM

Confirmations

6,593,104

Merkle Root

234d7983e4b134e035d6bad9ee6d226971e4e7691c95e134ae55996f0040a6d1

Transactions (2)

Coinbase2f8daee095d3dd…b40a8ffb7d3373

1 in → 1 out10.2200 XPM109 B

AXZyYAsL…mSHBmhk2

43581dcafb183d…97d977abb71e3a

8 in → 1 out82.0000 XPM957 B

AdPcJirK…3XgpV9WL

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.

5.788 × 10⁹²(93-digit number)

57886085601689061170…30314749908126935200

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

5.788 × 10⁹²(93-digit number)

57886085601689061170…30314749908126935199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.788 × 10⁹²(93-digit number)

57886085601689061170…30314749908126935201

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

1.157 × 10⁹³(94-digit number)

11577217120337812234…60629499816253870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.157 × 10⁹³(94-digit number)

11577217120337812234…60629499816253870401

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

2.315 × 10⁹³(94-digit number)

23154434240675624468…21258999632507740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.315 × 10⁹³(94-digit number)

23154434240675624468…21258999632507740801

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

4.630 × 10⁹³(94-digit number)

46308868481351248936…42517999265015481599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.630 × 10⁹³(94-digit number)

46308868481351248936…42517999265015481601

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

9.261 × 10⁹³(94-digit number)

92617736962702497872…85035998530030963199

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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 201401

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock af820bb7bea50637cbf84d7ff5a8c6a44fc759e40ac6609f9c79183fb8e0b518

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #201,401 on Chainz ↗