Home/Chain Registry/Block #88,161

Block #88,161

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 10:06:08 AM · Difficulty 9.2726 · 6,701,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26ce68ff0e7740bd2bc87bd2c6e4653c2dd390b453d8d9d37663c7c26485d64d

View on Chainz ↗

Height

#88,161

Difficulty

9.272578

Transactions

Size

206 B

Version

Bits

0945c7ac

Nonce

113,285

Timestamp

7/29/2013, 10:06:08 AM

Confirmations

6,701,883

Merkle Root

9b398e3ba7b6e60830e378936ffb2e6e18c8cd589df98b98971a71ee3542e193

Transactions (1)

Coinbase9b398e3ba7b6e6…1a71ee3542e193

1 in → 1 out11.6100 XPM109 B

AQdgBN3U…LVxQMGrr

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.

6.011 × 10¹¹⁰(111-digit number)

60116410158280081224…70820613546562825350

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

6.011 × 10¹¹⁰(111-digit number)

60116410158280081224…70820613546562825349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.011 × 10¹¹⁰(111-digit number)

60116410158280081224…70820613546562825351

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

1.202 × 10¹¹¹(112-digit number)

12023282031656016244…41641227093125650699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.202 × 10¹¹¹(112-digit number)

12023282031656016244…41641227093125650701

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

2.404 × 10¹¹¹(112-digit number)

24046564063312032489…83282454186251301399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.404 × 10¹¹¹(112-digit number)

24046564063312032489…83282454186251301401

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

4.809 × 10¹¹¹(112-digit number)

48093128126624064979…66564908372502602799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.809 × 10¹¹¹(112-digit number)

48093128126624064979…66564908372502602801

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

9.618 × 10¹¹¹(112-digit number)

96186256253248129959…33129816745005205599

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 88161

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 26ce68ff0e7740bd2bc87bd2c6e4653c2dd390b453d8d9d37663c7c26485d64d

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 #88,161 on Chainz ↗