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Block #314,710

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2013, 3:04:03 AM Β· Difficulty 10.0712 Β· 6,488,929 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df8be0896ecfe69105ceb9d4e8e52f1d569a7673865bcc8ea218f64ca57ca256
View on Chainz β†—

Height

#314,710

Difficulty

10.071150

Transactions

1

Size

207 B

Version

2

Bits

0a1236e9

Nonce

7,524

Timestamp

12/16/2013, 3:04:03 AM

Confirmations

6,488,929

Merkle Root

494d16fa598fa2fb2f8c7588c7d2d4b1802f274a4da9e90008e2dfc74e933ad3
Transactions (1)
Coinbase494d16fa598fa2…e2dfc74e933ad3
1 in β†’ 1 out9.8400 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.

8.042 Γ— 10⁹⁡(96-digit number)
80420144971314143334…16467993093473684480
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
8.042 Γ— 10⁹⁡(96-digit number)
80420144971314143334…16467993093473684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.608 Γ— 10⁹⁢(97-digit number)
16084028994262828666…32935986186947368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.216 Γ— 10⁹⁢(97-digit number)
32168057988525657333…65871972373894737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.433 Γ— 10⁹⁢(97-digit number)
64336115977051314667…31743944747789475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.286 Γ— 10⁹⁷(98-digit number)
12867223195410262933…63487889495578951681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.573 Γ— 10⁹⁷(98-digit number)
25734446390820525867…26975778991157903361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.146 Γ— 10⁹⁷(98-digit number)
51468892781641051734…53951557982315806721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.029 Γ— 10⁹⁸(99-digit number)
10293778556328210346…07903115964631613441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.058 Γ— 10⁹⁸(99-digit number)
20587557112656420693…15806231929263226881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.117 Γ— 10⁹⁸(99-digit number)
41175114225312841387…31612463858526453761
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 314710

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 df8be0896ecfe69105ceb9d4e8e52f1d569a7673865bcc8ea218f64ca57ca256

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 #314,710 on Chainz β†—
Circulating Supply:57,673,143 XPMΒ·at block #6,803,638 Β· updates every 60s
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