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Block #402,547

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/13/2014, 12:35:40 PM Β· Difficulty 10.4368 Β· 6,397,663 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a9c99b3f1bfedf41b9ea6a668bdca0147cfc60d287831857ad2d926fbcaf7751
View on Chainz β†—

Height

#402,547

Difficulty

10.436825

Transactions

1

Size

188 B

Version

2

Bits

0a6fd3c0

Nonce

481,821

Timestamp

2/13/2014, 12:35:40 PM

Confirmations

6,397,663

Merkle Root

2cea83a88886517ef0010fe354c76e25d6f62e676e412a668c3959dece812f4c
Transactions (1)
Coinbase2cea83a8888651…3959dece812f4c
1 in β†’ 1 out9.1700 XPM97 B
AKxxLGqh…oySJc6b5
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.

4.895 Γ— 10⁹⁷(98-digit number)
48951563930371229163…21101442443010928640
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
4.895 Γ— 10⁹⁷(98-digit number)
48951563930371229163…21101442443010928639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.790 Γ— 10⁹⁷(98-digit number)
97903127860742458326…42202884886021857279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁸(99-digit number)
19580625572148491665…84405769772043714559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.916 Γ— 10⁹⁸(99-digit number)
39161251144296983330…68811539544087429119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.832 Γ— 10⁹⁸(99-digit number)
78322502288593966661…37623079088174858239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.566 Γ— 10⁹⁹(100-digit number)
15664500457718793332…75246158176349716479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.132 Γ— 10⁹⁹(100-digit number)
31329000915437586664…50492316352699432959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.265 Γ— 10⁹⁹(100-digit number)
62658001830875173329…00984632705398865919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.253 Γ— 10¹⁰⁰(101-digit number)
12531600366175034665…01969265410797731839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.506 Γ— 10¹⁰⁰(101-digit number)
25063200732350069331…03938530821595463679
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 402547

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 a9c99b3f1bfedf41b9ea6a668bdca0147cfc60d287831857ad2d926fbcaf7751

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 #402,547 on Chainz β†—
Circulating Supply:57,645,749 XPMΒ·at block #6,800,209 Β· updates every 60s
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