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Block #438,712

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/11/2014, 5:14:01 AM Β· Difficulty 10.3545 Β· 6,388,431 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2702679e540b539b433adf5fb59e9747aa8ac7733990249c8ea93ad0ef4b8ce
View on Chainz β†—

Height

#438,712

Difficulty

10.354542

Transactions

1

Size

207 B

Version

2

Bits

0a5ac346

Nonce

4,094

Timestamp

3/11/2014, 5:14:01 AM

Confirmations

6,388,431

Merkle Root

01d2ab657dde8a5a5200fa12ab7bfa77301c838089ceb26d6d4c80dde0c5c98c
Transactions (1)
Coinbase01d2ab657dde8a…4c80dde0c5c98c
1 in β†’ 1 out9.3100 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.

5.203 Γ— 10⁹⁷(98-digit number)
52034046237225559662…82141494710725757760
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
5.203 Γ— 10⁹⁷(98-digit number)
52034046237225559662…82141494710725757759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.040 Γ— 10⁹⁸(99-digit number)
10406809247445111932…64282989421451515519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.081 Γ— 10⁹⁸(99-digit number)
20813618494890223864…28565978842903031039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.162 Γ— 10⁹⁸(99-digit number)
41627236989780447729…57131957685806062079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.325 Γ— 10⁹⁸(99-digit number)
83254473979560895459…14263915371612124159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.665 Γ— 10⁹⁹(100-digit number)
16650894795912179091…28527830743224248319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.330 Γ— 10⁹⁹(100-digit number)
33301789591824358183…57055661486448496639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.660 Γ— 10⁹⁹(100-digit number)
66603579183648716367…14111322972896993279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.332 Γ— 10¹⁰⁰(101-digit number)
13320715836729743273…28222645945793986559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.664 Γ— 10¹⁰⁰(101-digit number)
26641431673459486547…56445291891587973119
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 438712

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 d2702679e540b539b433adf5fb59e9747aa8ac7733990249c8ea93ad0ef4b8ce

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 #438,712 on Chainz β†—
Circulating Supply:57,861,326 XPMΒ·at block #6,827,142 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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