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Block #170,291

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2013, 4:12:07 PM Β· Difficulty 9.8655 Β· 6,629,731 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0b9ef710293ba644ea24fedbf43be9cd39067abacb8bc77aac15752ca29754a9
View on Chainz β†—

Height

#170,291

Difficulty

9.865513

Transactions

1

Size

198 B

Version

2

Bits

09dd9242

Nonce

82,193

Timestamp

9/18/2013, 4:12:07 PM

Confirmations

6,629,731

Merkle Root

7dfc8ff3f601770efffcdea22fd99b5d5186d2ee434338abd572ab47bb92ac1c
Transactions (1)
Coinbase7dfc8ff3f60177…72ab47bb92ac1c
1 in β†’ 1 out10.2600 XPM109 B
AJQ7bqzh…oY2ANRaW
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.

5.813 Γ— 10⁹²(93-digit number)
58138495559053257923…41554749998073573890
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
5.813 Γ— 10⁹²(93-digit number)
58138495559053257923…41554749998073573889
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.162 Γ— 10⁹³(94-digit number)
11627699111810651584…83109499996147147779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.325 Γ— 10⁹³(94-digit number)
23255398223621303169…66218999992294295559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.651 Γ— 10⁹³(94-digit number)
46510796447242606338…32437999984588591119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.302 Γ— 10⁹³(94-digit number)
93021592894485212677…64875999969177182239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.860 Γ— 10⁹⁴(95-digit number)
18604318578897042535…29751999938354364479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.720 Γ— 10⁹⁴(95-digit number)
37208637157794085070…59503999876708728959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.441 Γ— 10⁹⁴(95-digit number)
74417274315588170141…19007999753417457919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.488 Γ— 10⁹⁡(96-digit number)
14883454863117634028…38015999506834915839
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 170291

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 0b9ef710293ba644ea24fedbf43be9cd39067abacb8bc77aac15752ca29754a9

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 #170,291 on Chainz β†—
Circulating Supply:57,644,232 XPMΒ·at block #6,800,021 Β· updates every 60s
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