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Block #116,525

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/14/2013, 11:33:38 AM Β· Difficulty 9.7484 Β· 6,710,481 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
84a05d6155db805b72cdd98e5a5bf6a95eab90054095edadef81a14f9e9d645a
View on Chainz β†—

Height

#116,525

Difficulty

9.748388

Transactions

2

Size

356 B

Version

2

Bits

09bf9655

Nonce

663,526

Timestamp

8/14/2013, 11:33:38 AM

Confirmations

6,710,481

Merkle Root

b1019cc3d411cb17f9e79fe7fff9b4f720895866dedafd82f0b6f2b7a7fcad3f
Transactions (2)
Coinbased45b94688dae41…1476e192108278
1 in β†’ 1 out10.5200 XPM109 B
AbrjnRqA…rfU9YBk2
67471d79ccff66…32c43924467855
1 in β†’ 1 out10.7000 XPM157 B
AdaPyCyZ…F83yVpEB
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.131 Γ— 10⁹⁡(96-digit number)
11319693292739403781…38237742987242340860
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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.

1
origin βˆ’ 1
1.131 Γ— 10⁹⁡(96-digit number)
11319693292739403781…38237742987242340859
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.263 Γ— 10⁹⁡(96-digit number)
22639386585478807563…76475485974484681719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.527 Γ— 10⁹⁡(96-digit number)
45278773170957615127…52950971948969363439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.055 Γ— 10⁹⁡(96-digit number)
90557546341915230254…05901943897938726879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.811 Γ— 10⁹⁢(97-digit number)
18111509268383046050…11803887795877453759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.622 Γ— 10⁹⁢(97-digit number)
36223018536766092101…23607775591754907519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.244 Γ— 10⁹⁢(97-digit number)
72446037073532184203…47215551183509815039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.448 Γ— 10⁹⁷(98-digit number)
14489207414706436840…94431102367019630079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.897 Γ— 10⁹⁷(98-digit number)
28978414829412873681…88862204734039260159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” 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 β†’
β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 116525

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 84a05d6155db805b72cdd98e5a5bf6a95eab90054095edadef81a14f9e9d645a

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 β†’ Debug Window β†’ 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 #116,525 on Chainz β†—
Circulating Supply:57,860,224 XPMΒ·at block #6,827,005 Β· updates every 60s
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