Home/Chain Registry/Block #115,184

Block #115,184

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/13/2013, 3:04:23 PM · Difficulty 9.7427 · 6,676,433 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c486d8ddb1dbc4d3c91fc2d01282f43da28e6a278647d526e2db02891174e8cc

View on Chainz ↗

Height

#115,184

Difficulty

9.742651

Transactions

Size

1.54 KB

Version

Bits

09be1e5a

Nonce

293,778

Timestamp

8/13/2013, 3:04:23 PM

Confirmations

6,676,433

Merkle Root

dd41eeff7c3ed577709b3d8353dd666f142a59dc8c8a991ec0a59299bdbf09b3

Transactions (2)

Coinbasede777d0acf662b…4964f286e96632

1 in → 1 out10.5400 XPM109 B

AJAEMCng…kE6MBAC1

a1096d06cd075d…7283891fbbc7b4

9 in → 1 out18.1432 XPM1.34 KB

AWzkEpia…952sWSKb

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.

1.222 × 10⁹⁴(95-digit number)

12227340351024679122…80796795455146786520

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

1.222 × 10⁹⁴(95-digit number)

12227340351024679122…80796795455146786519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.222 × 10⁹⁴(95-digit number)

12227340351024679122…80796795455146786521

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

2.445 × 10⁹⁴(95-digit number)

24454680702049358244…61593590910293573039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.445 × 10⁹⁴(95-digit number)

24454680702049358244…61593590910293573041

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

4.890 × 10⁹⁴(95-digit number)

48909361404098716489…23187181820587146079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.890 × 10⁹⁴(95-digit number)

48909361404098716489…23187181820587146081

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

9.781 × 10⁹⁴(95-digit number)

97818722808197432978…46374363641174292159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.781 × 10⁹⁴(95-digit number)

97818722808197432978…46374363641174292161

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

1.956 × 10⁹⁵(96-digit number)

19563744561639486595…92748727282348584319

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 115184

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 c486d8ddb1dbc4d3c91fc2d01282f43da28e6a278647d526e2db02891174e8cc

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 #115,184 on Chainz ↗