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Block #453,193

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/21/2014, 2:34:48 AM Β· Difficulty 10.3928 Β· 6,377,486 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b868bc074dd9404cdfe0b201dc4e2fdb818302b8d9d6b699564015988d2d2236
View on Chainz β†—

Height

#453,193

Difficulty

10.392765

Transactions

1

Size

199 B

Version

2

Bits

0a648c41

Nonce

58,795

Timestamp

3/21/2014, 2:34:48 AM

Confirmations

6,377,486

Merkle Root

72523e158cc37c21c7ea08a77a89a038b1e4f4383e1fdf0a0164f8563413cab5
Transactions (1)
Coinbase72523e158cc37c…64f8563413cab5
1 in β†’ 1 out9.2400 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.

2.960 Γ— 10⁹³(94-digit number)
29606161245114524030…87973728550838131200
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.960 Γ— 10⁹³(94-digit number)
29606161245114524030…87973728550838131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.921 Γ— 10⁹³(94-digit number)
59212322490229048060…75947457101676262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.184 Γ— 10⁹⁴(95-digit number)
11842464498045809612…51894914203352524801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.368 Γ— 10⁹⁴(95-digit number)
23684928996091619224…03789828406705049601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.736 Γ— 10⁹⁴(95-digit number)
47369857992183238448…07579656813410099201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.473 Γ— 10⁹⁴(95-digit number)
94739715984366476896…15159313626820198401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.894 Γ— 10⁹⁡(96-digit number)
18947943196873295379…30318627253640396801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.789 Γ— 10⁹⁡(96-digit number)
37895886393746590758…60637254507280793601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.579 Γ— 10⁹⁡(96-digit number)
75791772787493181517…21274509014561587201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.515 Γ— 10⁹⁢(97-digit number)
15158354557498636303…42549018029123174401
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 453193

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 b868bc074dd9404cdfe0b201dc4e2fdb818302b8d9d6b699564015988d2d2236

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 #453,193 on Chainz β†—
Circulating Supply:57,889,562 XPMΒ·at block #6,830,678 Β· updates every 60s
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