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Block #391,113

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/5/2014, 2:42:50 PM Β· Difficulty 10.4281 Β· 6,421,519 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a495886c6ad115af9cf57e7b14a5fadb7ee0f4c3045d21e1e45dcf1cea2363b
View on Chainz β†—

Height

#391,113

Difficulty

10.428133

Transactions

1

Size

202 B

Version

2

Bits

0a6d9a19

Nonce

24,411

Timestamp

2/5/2014, 2:42:50 PM

Confirmations

6,421,519

Merkle Root

548e84ad93762ce9dadb94a9f20e70d2c7bc98c6d80c5b4a892c5b60e89cd946
Transactions (1)
Coinbase548e84ad93762c…2c5b60e89cd946
1 in β†’ 1 out9.1800 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.

5.600 Γ— 10⁹⁸(99-digit number)
56003241502370122185…33526057663822161840
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
5.600 Γ— 10⁹⁸(99-digit number)
56003241502370122185…33526057663822161839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.120 Γ— 10⁹⁹(100-digit number)
11200648300474024437…67052115327644323679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.240 Γ— 10⁹⁹(100-digit number)
22401296600948048874…34104230655288647359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.480 Γ— 10⁹⁹(100-digit number)
44802593201896097748…68208461310577294719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.960 Γ— 10⁹⁹(100-digit number)
89605186403792195497…36416922621154589439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.792 Γ— 10¹⁰⁰(101-digit number)
17921037280758439099…72833845242309178879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.584 Γ— 10¹⁰⁰(101-digit number)
35842074561516878198…45667690484618357759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.168 Γ— 10¹⁰⁰(101-digit number)
71684149123033756397…91335380969236715519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.433 Γ— 10¹⁰¹(102-digit number)
14336829824606751279…82670761938473431039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.867 Γ— 10¹⁰¹(102-digit number)
28673659649213502559…65341523876946862079
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 391113

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 3a495886c6ad115af9cf57e7b14a5fadb7ee0f4c3045d21e1e45dcf1cea2363b

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 #391,113 on Chainz β†—
Circulating Supply:57,745,093 XPMΒ·at block #6,812,631 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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