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Block #345,170

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/5/2014, 6:16:51 PM Β· Difficulty 10.2087 Β· 6,480,311 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eecfabc3075b645c655a225e74171a4a45e4cf1a395e309d66cb892296d24dce
View on Chainz β†—

Height

#345,170

Difficulty

10.208656

Transactions

1

Size

206 B

Version

2

Bits

0a356a81

Nonce

299,575

Timestamp

1/5/2014, 6:16:51 PM

Confirmations

6,480,311

Merkle Root

96ed0147da9519005823a3034e299b797ee3739fa6febe3b6d1581f750df05fc
Transactions (1)
Coinbase96ed0147da9519…1581f750df05fc
1 in β†’ 1 out9.5800 XPM116 B
AbwWkWZt…kawDhufa
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.

7.069 Γ— 10⁹³(94-digit number)
70690836632934310112…88000409927272803350
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
7.069 Γ— 10⁹³(94-digit number)
70690836632934310112…88000409927272803351
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.413 Γ— 10⁹⁴(95-digit number)
14138167326586862022…76000819854545606701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.827 Γ— 10⁹⁴(95-digit number)
28276334653173724045…52001639709091213401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.655 Γ— 10⁹⁴(95-digit number)
56552669306347448090…04003279418182426801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.131 Γ— 10⁹⁡(96-digit number)
11310533861269489618…08006558836364853601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.262 Γ— 10⁹⁡(96-digit number)
22621067722538979236…16013117672729707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.524 Γ— 10⁹⁡(96-digit number)
45242135445077958472…32026235345459414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.048 Γ— 10⁹⁡(96-digit number)
90484270890155916944…64052470690918828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.809 Γ— 10⁹⁢(97-digit number)
18096854178031183388…28104941381837657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.619 Γ— 10⁹⁢(97-digit number)
36193708356062366777…56209882763675315201
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 345170

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 eecfabc3075b645c655a225e74171a4a45e4cf1a395e309d66cb892296d24dce

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 #345,170 on Chainz β†—
Circulating Supply:57,847,942 XPMΒ·at block #6,825,480 Β· updates every 60s
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