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Home/Chain Registry/Block #316,981

Block #316,981

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2013, 9:33:43 AM Β· Difficulty 10.1495 Β· 6,492,198 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5861a0085dcccfde6746db86fb06326040b1f51b2c9a3bb54521d2fe9cc03e0e
View on Chainz β†—

Height

#316,981

Difficulty

10.149489

Transactions

1

Size

203 B

Version

2

Bits

0a2644e5

Nonce

227,849

Timestamp

12/17/2013, 9:33:43 AM

Confirmations

6,492,198

Merkle Root

dac440cc95445fe3373ddb2d11cb30cc0ffe417c7a7357c0337c28facab15d5d
Transactions (1)
Coinbasedac440cc95445f…7c28facab15d5d
1 in β†’ 1 out9.6900 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.

4.588 Γ— 10¹⁰⁰(101-digit number)
45888976511423707456…82694779209090073600
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
4.588 Γ— 10¹⁰⁰(101-digit number)
45888976511423707456…82694779209090073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.177 Γ— 10¹⁰⁰(101-digit number)
91777953022847414913…65389558418180147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.835 Γ— 10¹⁰¹(102-digit number)
18355590604569482982…30779116836360294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.671 Γ— 10¹⁰¹(102-digit number)
36711181209138965965…61558233672720588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.342 Γ— 10¹⁰¹(102-digit number)
73422362418277931930…23116467345441177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.468 Γ— 10¹⁰²(103-digit number)
14684472483655586386…46232934690882355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.936 Γ— 10¹⁰²(103-digit number)
29368944967311172772…92465869381764710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.873 Γ— 10¹⁰²(103-digit number)
58737889934622345544…84931738763529420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.174 Γ— 10¹⁰³(104-digit number)
11747577986924469108…69863477527058841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.349 Γ— 10¹⁰³(104-digit number)
23495155973848938217…39726955054117683201
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 316981

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 5861a0085dcccfde6746db86fb06326040b1f51b2c9a3bb54521d2fe9cc03e0e

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 #316,981 on Chainz β†—
Circulating Supply:57,717,496 XPMΒ·at block #6,809,178 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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