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Block #429,389

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/4/2014, 6:07:57 PM Β· Difficulty 10.3473 Β· 6,397,380 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0472b64ff205fde15bc92b793b9640dc53ebbc02b4452ddc7886f57df757e2e
View on Chainz β†—

Height

#429,389

Difficulty

10.347282

Transactions

2

Size

427 B

Version

2

Bits

0a58e781

Nonce

38,028

Timestamp

3/4/2014, 6:07:57 PM

Confirmations

6,397,380

Merkle Root

fe883c371afdc0f597237b50eccee5a5a10a4f5747cab134500d2834928a7f67
Transactions (2)
Coinbase2587ec7ef32940…1227c1c943dcbf
1 in β†’ 1 out9.3400 XPM110 B
AeKNrjNj…1NEq95Ta
40f25faec83096…ef079480a664e4
1 in β†’ 2 out2.7727 XPM226 B
ATUquBS2…P9NkGmMLASizZgzZ…3wDzLpyL
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.

1.384 Γ— 10⁹⁸(99-digit number)
13844313108382414844…02295595081102231840
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
1.384 Γ— 10⁹⁸(99-digit number)
13844313108382414844…02295595081102231839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.768 Γ— 10⁹⁸(99-digit number)
27688626216764829688…04591190162204463679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.537 Γ— 10⁹⁸(99-digit number)
55377252433529659376…09182380324408927359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.107 Γ— 10⁹⁹(100-digit number)
11075450486705931875…18364760648817854719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.215 Γ— 10⁹⁹(100-digit number)
22150900973411863750…36729521297635709439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.430 Γ— 10⁹⁹(100-digit number)
44301801946823727501…73459042595271418879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.860 Γ— 10⁹⁹(100-digit number)
88603603893647455002…46918085190542837759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.772 Γ— 10¹⁰⁰(101-digit number)
17720720778729491000…93836170381085675519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.544 Γ— 10¹⁰⁰(101-digit number)
35441441557458982001…87672340762171351039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.088 Γ— 10¹⁰⁰(101-digit number)
70882883114917964002…75344681524342702079
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 429389

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 e0472b64ff205fde15bc92b793b9640dc53ebbc02b4452ddc7886f57df757e2e

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 #429,389 on Chainz β†—
Circulating Supply:57,858,313 XPMΒ·at block #6,826,768 Β· updates every 60s
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