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Block #313,580

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/15/2013, 1:12:16 PM Β· Difficulty 10.0144 Β· 6,490,417 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e9d934c39642957409d303590982ddfaa0c3611643220f6aad4577076d862509
View on Chainz β†—

Height

#313,580

Difficulty

10.014354

Transactions

1

Size

207 B

Version

2

Bits

0a03acb8

Nonce

33,556,292

Timestamp

12/15/2013, 1:12:16 PM

Confirmations

6,490,417

Merkle Root

4cb7d751b80a799458e801b5dacf0776299b3c5f885cd15006f7afb5451ef0cf
Transactions (1)
Coinbase4cb7d751b80a79…f7afb5451ef0cf
1 in β†’ 1 out9.9600 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.

7.328 Γ— 10⁹⁡(96-digit number)
73283319224434936235…84203894831892956160
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
7.328 Γ— 10⁹⁡(96-digit number)
73283319224434936235…84203894831892956159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.465 Γ— 10⁹⁢(97-digit number)
14656663844886987247…68407789663785912319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.931 Γ— 10⁹⁢(97-digit number)
29313327689773974494…36815579327571824639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.862 Γ— 10⁹⁢(97-digit number)
58626655379547948988…73631158655143649279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.172 Γ— 10⁹⁷(98-digit number)
11725331075909589797…47262317310287298559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.345 Γ— 10⁹⁷(98-digit number)
23450662151819179595…94524634620574597119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.690 Γ— 10⁹⁷(98-digit number)
46901324303638359191…89049269241149194239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.380 Γ— 10⁹⁷(98-digit number)
93802648607276718382…78098538482298388479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.876 Γ— 10⁹⁸(99-digit number)
18760529721455343676…56197076964596776959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.752 Γ— 10⁹⁸(99-digit number)
37521059442910687352…12394153929193553919
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 313580

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 e9d934c39642957409d303590982ddfaa0c3611643220f6aad4577076d862509

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 #313,580 on Chainz β†—
Circulating Supply:57,676,024 XPMΒ·at block #6,803,996 Β· updates every 60s
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