Home/Chain Registry/Block #171,318

Block #171,318

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/19/2013, 10:05:16 AM · Difficulty 9.8644 · 6,629,021 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ebb482b19f11806ab280eaa2b8a4ba5fec05fabb6a57d59c50e549e7ff97c06

View on Chainz ↗

Height

#171,318

Difficulty

9.864394

Transactions

Size

684 B

Version

Bits

09dd48f2

Nonce

94,967

Timestamp

9/19/2013, 10:05:16 AM

Confirmations

6,629,021

Merkle Root

d5f1b2265c0e771d45cb3514d158ee8ea89703a9519e672ac4ee610c27e5c1a6

Transactions (3)

Coinbase59218b1cc0f7b2…13342ccbfbc8d5

1 in → 1 out10.2800 XPM109 B

AH7Lo2f3…5MaXhQSd

aeaebe223780ec…483c35b01643a2

1 in → 3 out10.2400 XPM226 B

ARArekiX…iTsUsz9L AHRnoPQw…SLFKBYxM AUT1qxTx…t5B3qd8Z

041c1aeff021b5…529ac8201423b5

1 in → 3 out7.1558 XPM259 B

AKpspM1U…4AY1x9pP ARUxjsct…PGMSTrZ5 APzXdCRz…gsaGkBeW

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.

3.632 × 10⁹⁵(96-digit number)

36323041167034387795…77791854360485576960

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

3.632 × 10⁹⁵(96-digit number)

36323041167034387795…77791854360485576959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.632 × 10⁹⁵(96-digit number)

36323041167034387795…77791854360485576961

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

7.264 × 10⁹⁵(96-digit number)

72646082334068775591…55583708720971153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.264 × 10⁹⁵(96-digit number)

72646082334068775591…55583708720971153921

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

1.452 × 10⁹⁶(97-digit number)

14529216466813755118…11167417441942307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.452 × 10⁹⁶(97-digit number)

14529216466813755118…11167417441942307841

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

2.905 × 10⁹⁶(97-digit number)

29058432933627510236…22334834883884615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.905 × 10⁹⁶(97-digit number)

29058432933627510236…22334834883884615681

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

5.811 × 10⁹⁶(97-digit number)

58116865867255020473…44669669767769231359

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 171318

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 3ebb482b19f11806ab280eaa2b8a4ba5fec05fabb6a57d59c50e549e7ff97c06

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 #171,318 on Chainz ↗