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Home/Chain Registry/Block #310,982

Block #310,982

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/14/2013, 8:24:19 AM Β· Difficulty 9.9953 Β· 6,532,151 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5489db45e33e3661c266fbbfae0089933365ff64985f9ba1da872a38178f36d7
View on Chainz β†—

Height

#310,982

Difficulty

9.995342

Transactions

1

Size

207 B

Version

2

Bits

09fecec2

Nonce

83,889,182

Timestamp

12/14/2013, 8:24:19 AM

Confirmations

6,532,151

Merkle Root

089b817dc074f5bfbbf92646d7cd5ded503f17dc8f7878cbee49162f3aeddb2f
Transactions (1)
Coinbase089b817dc074f5…49162f3aeddb2f
1 in β†’ 1 out9.9900 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.

1.552 Γ— 10⁹⁢(97-digit number)
15528248223259090850…19163152099350340800
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
1.552 Γ— 10⁹⁢(97-digit number)
15528248223259090850…19163152099350340799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.105 Γ— 10⁹⁢(97-digit number)
31056496446518181700…38326304198700681599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.211 Γ— 10⁹⁢(97-digit number)
62112992893036363400…76652608397401363199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.242 Γ— 10⁹⁷(98-digit number)
12422598578607272680…53305216794802726399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.484 Γ— 10⁹⁷(98-digit number)
24845197157214545360…06610433589605452799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.969 Γ— 10⁹⁷(98-digit number)
49690394314429090720…13220867179210905599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.938 Γ— 10⁹⁷(98-digit number)
99380788628858181441…26441734358421811199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.987 Γ— 10⁹⁸(99-digit number)
19876157725771636288…52883468716843622399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.975 Γ— 10⁹⁸(99-digit number)
39752315451543272576…05766937433687244799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.950 Γ— 10⁹⁸(99-digit number)
79504630903086545152…11533874867374489599
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 310982

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 5489db45e33e3661c266fbbfae0089933365ff64985f9ba1da872a38178f36d7

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 #310,982 on Chainz β†—
Circulating Supply:57,989,427 XPMΒ·at block #6,843,132 Β· updates every 60s
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