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Block #409,528

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/18/2014, 10:38:14 AM Β· Difficulty 10.4283 Β· 6,416,916 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dfce80de253f31858afddb2d9a8d55ebdb8dc1d322a3893936596d22142dfb7d
View on Chainz β†—

Height

#409,528

Difficulty

10.428277

Transactions

1

Size

207 B

Version

2

Bits

0a6da389

Nonce

12,172

Timestamp

2/18/2014, 10:38:14 AM

Confirmations

6,416,916

Merkle Root

ff28e082be1e1d623219c5d22ca6ba96e7f0c4d6ad548c830b99209dbb7cfa7b
Transactions (1)
Coinbaseff28e082be1e1d…99209dbb7cfa7b
1 in β†’ 1 out9.1800 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.

7.492 Γ— 10⁹⁷(98-digit number)
74924854531672310831…70644801220899373600
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
7.492 Γ— 10⁹⁷(98-digit number)
74924854531672310831…70644801220899373599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.498 Γ— 10⁹⁸(99-digit number)
14984970906334462166…41289602441798747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.996 Γ— 10⁹⁸(99-digit number)
29969941812668924332…82579204883597494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.993 Γ— 10⁹⁸(99-digit number)
59939883625337848664…65158409767194988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.198 Γ— 10⁹⁹(100-digit number)
11987976725067569732…30316819534389977599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.397 Γ— 10⁹⁹(100-digit number)
23975953450135139465…60633639068779955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.795 Γ— 10⁹⁹(100-digit number)
47951906900270278931…21267278137559910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.590 Γ— 10⁹⁹(100-digit number)
95903813800540557863…42534556275119820799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.918 Γ— 10¹⁰⁰(101-digit number)
19180762760108111572…85069112550239641599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.836 Γ— 10¹⁰⁰(101-digit number)
38361525520216223145…70138225100479283199
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 409528

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 dfce80de253f31858afddb2d9a8d55ebdb8dc1d322a3893936596d22142dfb7d

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 #409,528 on Chainz β†—
Circulating Supply:57,855,689 XPMΒ·at block #6,826,443 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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