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Block #437,444

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/10/2014, 7:37:51 AM Β· Difficulty 10.3574 Β· 6,389,258 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9be513b0d7a16f24e8fc26549d7cdd1cb1e910605d8f0cc6a355871e428c9c8
View on Chainz β†—

Height

#437,444

Difficulty

10.357357

Transactions

1

Size

200 B

Version

2

Bits

0a5b7bc2

Nonce

91,314

Timestamp

3/10/2014, 7:37:51 AM

Confirmations

6,389,258

Merkle Root

22e578e700110385905f2f46746daeda4b0c9f537c1e1efcf8c5b097bebfeab0
Transactions (1)
Coinbase22e578e7001103…c5b097bebfeab0
1 in β†’ 1 out9.3100 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.

8.794 Γ— 10⁹³(94-digit number)
87942445680595453714…40899170453732003840
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
8.794 Γ— 10⁹³(94-digit number)
87942445680595453714…40899170453732003839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.758 Γ— 10⁹⁴(95-digit number)
17588489136119090742…81798340907464007679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.517 Γ— 10⁹⁴(95-digit number)
35176978272238181485…63596681814928015359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.035 Γ— 10⁹⁴(95-digit number)
70353956544476362971…27193363629856030719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.407 Γ— 10⁹⁡(96-digit number)
14070791308895272594…54386727259712061439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.814 Γ— 10⁹⁡(96-digit number)
28141582617790545188…08773454519424122879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.628 Γ— 10⁹⁡(96-digit number)
56283165235581090377…17546909038848245759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁢(97-digit number)
11256633047116218075…35093818077696491519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.251 Γ— 10⁹⁢(97-digit number)
22513266094232436150…70187636155392983039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.502 Γ— 10⁹⁢(97-digit number)
45026532188464872301…40375272310785966079
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 437444

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 d9be513b0d7a16f24e8fc26549d7cdd1cb1e910605d8f0cc6a355871e428c9c8

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 #437,444 on Chainz β†—
Circulating Supply:57,857,769 XPMΒ·at block #6,826,701 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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