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Block #394,542

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/8/2014, 1:01:47 AM Β· Difficulty 10.4215 Β· 6,406,894 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9799aa6802183a607d57fd2469a1f3672b2514a0fd2a1faddee729344e30f0a
View on Chainz β†—

Height

#394,542

Difficulty

10.421498

Transactions

1

Size

202 B

Version

2

Bits

0a6be753

Nonce

505,811

Timestamp

2/8/2014, 1:01:47 AM

Confirmations

6,406,894

Merkle Root

f797ee8d2a319c4f24c4fe394d19fe9cf43bed62adb2c0f5b2482ea8540c1da2
Transactions (1)
Coinbasef797ee8d2a319c…482ea8540c1da2
1 in β†’ 1 out9.1900 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.

9.700 Γ— 10⁹⁹(100-digit number)
97009562975423835104…62791764592602150400
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
9.700 Γ— 10⁹⁹(100-digit number)
97009562975423835104…62791764592602150399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.940 Γ— 10¹⁰⁰(101-digit number)
19401912595084767020…25583529185204300799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.880 Γ— 10¹⁰⁰(101-digit number)
38803825190169534041…51167058370408601599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.760 Γ— 10¹⁰⁰(101-digit number)
77607650380339068083…02334116740817203199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.552 Γ— 10¹⁰¹(102-digit number)
15521530076067813616…04668233481634406399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.104 Γ— 10¹⁰¹(102-digit number)
31043060152135627233…09336466963268812799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.208 Γ— 10¹⁰¹(102-digit number)
62086120304271254466…18672933926537625599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.241 Γ— 10¹⁰²(103-digit number)
12417224060854250893…37345867853075251199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.483 Γ— 10¹⁰²(103-digit number)
24834448121708501786…74691735706150502399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.966 Γ— 10¹⁰²(103-digit number)
49668896243417003573…49383471412301004799
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 394542

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 d9799aa6802183a607d57fd2469a1f3672b2514a0fd2a1faddee729344e30f0a

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 #394,542 on Chainz β†—
Circulating Supply:57,655,560 XPMΒ·at block #6,801,435 Β· updates every 60s
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