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Block #714,114

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2014, 7:17:03 PM Β· Difficulty 10.9555 Β· 6,080,697 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8e705e4de4df9b8ac8960b14128074e8c6e89394b42bb3f9595f8be21126eabe
View on Chainz β†—

Height

#714,114

Difficulty

10.955510

Transactions

1

Size

206 B

Version

2

Bits

0af49c4c

Nonce

132,647,804

Timestamp

9/9/2014, 7:17:03 PM

Confirmations

6,080,697

Merkle Root

81516cb7074aa40c4fd67110c7e9c2ebcf3d53710285353eae5098f1232abad3
Transactions (1)
Coinbase81516cb7074aa4…5098f1232abad3
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

5.537 Γ— 10⁹⁡(96-digit number)
55378326493287802656…88806123910313590400
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
5.537 Γ— 10⁹⁡(96-digit number)
55378326493287802656…88806123910313590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.107 Γ— 10⁹⁢(97-digit number)
11075665298657560531…77612247820627180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.215 Γ— 10⁹⁢(97-digit number)
22151330597315121062…55224495641254361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.430 Γ— 10⁹⁢(97-digit number)
44302661194630242125…10448991282508723199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.860 Γ— 10⁹⁢(97-digit number)
88605322389260484250…20897982565017446399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.772 Γ— 10⁹⁷(98-digit number)
17721064477852096850…41795965130034892799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.544 Γ— 10⁹⁷(98-digit number)
35442128955704193700…83591930260069785599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.088 Γ— 10⁹⁷(98-digit number)
70884257911408387400…67183860520139571199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.417 Γ— 10⁹⁸(99-digit number)
14176851582281677480…34367721040279142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.835 Γ— 10⁹⁸(99-digit number)
28353703164563354960…68735442080558284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.670 Γ— 10⁹⁸(99-digit number)
56707406329126709920…37470884161116569599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 714114

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 8e705e4de4df9b8ac8960b14128074e8c6e89394b42bb3f9595f8be21126eabe

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 #714,114 on Chainz β†—
Circulating Supply:57,602,534 XPMΒ·at block #6,794,810 Β· updates every 60s
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