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Block #316,396

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2013, 1:21:56 AM Β· Difficulty 10.1336 Β· 6,483,871 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f2f06a7b993fa8d430063af2741f4ef9d5a98582323869d5be17c36a6fbf3fb9
View on Chainz β†—

Height

#316,396

Difficulty

10.133591

Transactions

1

Size

205 B

Version

2

Bits

0a223302

Nonce

85,718

Timestamp

12/17/2013, 1:21:56 AM

Confirmations

6,483,871

Merkle Root

f25901dd5488475b764ecfc384783a9708e055a63ec972513b005f72bf1b8739
Transactions (1)
Coinbasef25901dd548847…005f72bf1b8739
1 in β†’ 1 out9.7200 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.

2.523 Γ— 10⁹³(94-digit number)
25239855837338237059…22550927392434120400
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
2.523 Γ— 10⁹³(94-digit number)
25239855837338237059…22550927392434120401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.047 Γ— 10⁹³(94-digit number)
50479711674676474119…45101854784868240801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.009 Γ— 10⁹⁴(95-digit number)
10095942334935294823…90203709569736481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.019 Γ— 10⁹⁴(95-digit number)
20191884669870589647…80407419139472963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.038 Γ— 10⁹⁴(95-digit number)
40383769339741179295…60814838278945926401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.076 Γ— 10⁹⁴(95-digit number)
80767538679482358590…21629676557891852801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.615 Γ— 10⁹⁡(96-digit number)
16153507735896471718…43259353115783705601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.230 Γ— 10⁹⁡(96-digit number)
32307015471792943436…86518706231567411201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.461 Γ— 10⁹⁡(96-digit number)
64614030943585886872…73037412463134822401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.292 Γ— 10⁹⁢(97-digit number)
12922806188717177374…46074824926269644801
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 316396

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 f2f06a7b993fa8d430063af2741f4ef9d5a98582323869d5be17c36a6fbf3fb9

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 #316,396 on Chainz β†—
Circulating Supply:57,646,193 XPMΒ·at block #6,800,266 Β· updates every 60s
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