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Block #233,085

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/29/2013, 12:18:33 PM Β· Difficulty 9.9421 Β· 6,562,654 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6d02b1141c2606996e5591e0528a731d2ac11ef736e509db0d8a2a0b94adef2d
View on Chainz β†—

Height

#233,085

Difficulty

9.942083

Transactions

1

Size

208 B

Version

2

Bits

09f12c62

Nonce

75,741

Timestamp

10/29/2013, 12:18:33 PM

Confirmations

6,562,654

Merkle Root

600c31d5016e6fc65413dd1f8e742fba891b0feb9140f6e4ae99c13f6a8d7976
Transactions (1)
Coinbase600c31d5016e6f…99c13f6a8d7976
1 in β†’ 1 out10.1000 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.

1.838 Γ— 10¹⁰⁰(101-digit number)
18387433501042009073…24690626276942385920
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
1.838 Γ— 10¹⁰⁰(101-digit number)
18387433501042009073…24690626276942385921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.677 Γ— 10¹⁰⁰(101-digit number)
36774867002084018147…49381252553884771841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.354 Γ— 10¹⁰⁰(101-digit number)
73549734004168036295…98762505107769543681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.470 Γ— 10¹⁰¹(102-digit number)
14709946800833607259…97525010215539087361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.941 Γ— 10¹⁰¹(102-digit number)
29419893601667214518…95050020431078174721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.883 Γ— 10¹⁰¹(102-digit number)
58839787203334429036…90100040862156349441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.176 Γ— 10¹⁰²(103-digit number)
11767957440666885807…80200081724312698881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.353 Γ— 10¹⁰²(103-digit number)
23535914881333771614…60400163448625397761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.707 Γ— 10¹⁰²(103-digit number)
47071829762667543229…20800326897250795521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.414 Γ— 10¹⁰²(103-digit number)
94143659525335086458…41600653794501591041
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 233085

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 6d02b1141c2606996e5591e0528a731d2ac11ef736e509db0d8a2a0b94adef2d

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 #233,085 on Chainz β†—
Circulating Supply:57,609,989 XPMΒ·at block #6,795,738 Β· updates every 60s
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