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Block #394,186

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/7/2014, 5:18:40 PM Β· Difficulty 10.4331 Β· 6,431,133 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
18fd7d0d40b572c530ecade2d792f064fd5710ea54bc0024ae0ddde0ec3fcd2d
View on Chainz β†—

Height

#394,186

Difficulty

10.433102

Transactions

1

Size

207 B

Version

2

Bits

0a6edfc5

Nonce

185,929

Timestamp

2/7/2014, 5:18:40 PM

Confirmations

6,431,133

Merkle Root

ecaf4f34cd51fa30aa6db5d0f9dd1c2368d19932a86a1de22f1c2e409cc0b230
Transactions (1)
Coinbaseecaf4f34cd51fa…1c2e409cc0b230
1 in β†’ 1 out9.1700 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.

4.520 Γ— 10⁹⁢(97-digit number)
45203096482161571939…80777939082175033360
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
4.520 Γ— 10⁹⁢(97-digit number)
45203096482161571939…80777939082175033359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.040 Γ— 10⁹⁢(97-digit number)
90406192964323143879…61555878164350066719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.808 Γ— 10⁹⁷(98-digit number)
18081238592864628775…23111756328700133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.616 Γ— 10⁹⁷(98-digit number)
36162477185729257551…46223512657400266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.232 Γ— 10⁹⁷(98-digit number)
72324954371458515103…92447025314800533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.446 Γ— 10⁹⁸(99-digit number)
14464990874291703020…84894050629601067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.892 Γ— 10⁹⁸(99-digit number)
28929981748583406041…69788101259202135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.785 Γ— 10⁹⁸(99-digit number)
57859963497166812083…39576202518404270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.157 Γ— 10⁹⁹(100-digit number)
11571992699433362416…79152405036808540159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.314 Γ— 10⁹⁹(100-digit number)
23143985398866724833…58304810073617080319
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 394186

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 18fd7d0d40b572c530ecade2d792f064fd5710ea54bc0024ae0ddde0ec3fcd2d

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 #394,186 on Chainz β†—
Circulating Supply:57,846,656 XPMΒ·at block #6,825,318 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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