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Block #246,133

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/5/2013, 10:00:07 PM Β· Difficulty 9.9644 Β· 6,596,129 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67e30a6b25e5d940cf13109008ae8a7ebf1198d0e861e34e261a634ad6480788
View on Chainz β†—

Height

#246,133

Difficulty

9.964359

Transactions

1

Size

209 B

Version

2

Bits

09f6e043

Nonce

16,777,882

Timestamp

11/5/2013, 10:00:07 PM

Confirmations

6,596,129

Merkle Root

3fd048f6953c764cfa19089c3e245fd27b1d111e7fbffaf1674c45d25ec2061e
Transactions (1)
Coinbase3fd048f6953c76…4c45d25ec2061e
1 in β†’ 1 out10.0600 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.

1.098 Γ— 10¹⁰³(104-digit number)
10980649587584833922…34482450750452531200
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
1.098 Γ— 10¹⁰³(104-digit number)
10980649587584833922…34482450750452531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.196 Γ— 10¹⁰³(104-digit number)
21961299175169667845…68964901500905062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.392 Γ— 10¹⁰³(104-digit number)
43922598350339335691…37929803001810124801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.784 Γ— 10¹⁰³(104-digit number)
87845196700678671383…75859606003620249601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.756 Γ— 10¹⁰⁴(105-digit number)
17569039340135734276…51719212007240499201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.513 Γ— 10¹⁰⁴(105-digit number)
35138078680271468553…03438424014480998401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.027 Γ— 10¹⁰⁴(105-digit number)
70276157360542937106…06876848028961996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.405 Γ— 10¹⁰⁡(106-digit number)
14055231472108587421…13753696057923993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.811 Γ— 10¹⁰⁡(106-digit number)
28110462944217174842…27507392115847987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.622 Γ— 10¹⁰⁡(106-digit number)
56220925888434349685…55014784231695974401
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 246133

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 67e30a6b25e5d940cf13109008ae8a7ebf1198d0e861e34e261a634ad6480788

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 #246,133 on Chainz β†—
Circulating Supply:57,982,494 XPMΒ·at block #6,842,261 Β· updates every 60s
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