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Block #208,151

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 8:38:29 PM Β· Difficulty 9.9051 Β· 6,597,070 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f3584b738a9b21c9b070aed3e4bc754022b42be9e5c590b0e40917fc9eaa455f
View on Chainz β†—

Height

#208,151

Difficulty

9.905149

Transactions

1

Size

209 B

Version

2

Bits

09e7b7e0

Nonce

15,832

Timestamp

10/13/2013, 8:38:29 PM

Confirmations

6,597,070

Merkle Root

473fd3c1759dd2478b5b2ba5fd7c750b8a1ef5d8545ca93681132abc2858eb10
Transactions (1)
Coinbase473fd3c1759dd2…132abc2858eb10
1 in β†’ 1 out10.1800 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.420 Γ— 10¹⁰⁰(101-digit number)
84203163660896224176…77728516923883760640
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
8.420 Γ— 10¹⁰⁰(101-digit number)
84203163660896224176…77728516923883760639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.684 Γ— 10¹⁰¹(102-digit number)
16840632732179244835…55457033847767521279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.368 Γ— 10¹⁰¹(102-digit number)
33681265464358489670…10914067695535042559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.736 Γ— 10¹⁰¹(102-digit number)
67362530928716979341…21828135391070085119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.347 Γ— 10¹⁰²(103-digit number)
13472506185743395868…43656270782140170239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.694 Γ— 10¹⁰²(103-digit number)
26945012371486791736…87312541564280340479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.389 Γ— 10¹⁰²(103-digit number)
53890024742973583473…74625083128560680959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.077 Γ— 10¹⁰³(104-digit number)
10778004948594716694…49250166257121361919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.155 Γ— 10¹⁰³(104-digit number)
21556009897189433389…98500332514242723839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.311 Γ— 10¹⁰³(104-digit number)
43112019794378866778…97000665028485447679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 208151

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 f3584b738a9b21c9b070aed3e4bc754022b42be9e5c590b0e40917fc9eaa455f

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 #208,151 on Chainz β†—
Circulating Supply:57,685,842 XPMΒ·at block #6,805,220 Β· updates every 60s
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