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Block #314,726

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2013, 3:18:37 AM Β· Difficulty 10.0715 Β· 6,486,821 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
36e2f7a09069fd25f79dae7b20c7d635d890dcb3db7bd85d08d80c27c64e7dfe
View on Chainz β†—

Height

#314,726

Difficulty

10.071502

Transactions

1

Size

200 B

Version

2

Bits

0a124dfa

Nonce

120,511

Timestamp

12/16/2013, 3:18:37 AM

Confirmations

6,486,821

Merkle Root

ef6e26747ee8d8ac615f4cccf77865ee1f6c6e6d707403a3350073ae36164b43
Transactions (1)
Coinbaseef6e26747ee8d8…0073ae36164b43
1 in β†’ 1 out9.8400 XPM110 B
AeKNrjNj…1NEq95Ta
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.

5.917 Γ— 10⁹⁴(95-digit number)
59174371316105572329…83934040017291901130
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
5.917 Γ— 10⁹⁴(95-digit number)
59174371316105572329…83934040017291901131
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.183 Γ— 10⁹⁡(96-digit number)
11834874263221114465…67868080034583802261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.366 Γ— 10⁹⁡(96-digit number)
23669748526442228931…35736160069167604521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.733 Γ— 10⁹⁡(96-digit number)
47339497052884457863…71472320138335209041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.467 Γ— 10⁹⁡(96-digit number)
94678994105768915726…42944640276670418081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.893 Γ— 10⁹⁢(97-digit number)
18935798821153783145…85889280553340836161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.787 Γ— 10⁹⁢(97-digit number)
37871597642307566290…71778561106681672321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.574 Γ— 10⁹⁢(97-digit number)
75743195284615132581…43557122213363344641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.514 Γ— 10⁹⁷(98-digit number)
15148639056923026516…87114244426726689281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.029 Γ— 10⁹⁷(98-digit number)
30297278113846053032…74228488853453378561
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 314726

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 36e2f7a09069fd25f79dae7b20c7d635d890dcb3db7bd85d08d80c27c64e7dfe

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 #314,726 on Chainz β†—
Circulating Supply:57,656,456 XPMΒ·at block #6,801,546 Β· updates every 60s
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