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Block #338,491

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/1/2014, 11:25:49 AM Β· Difficulty 10.1220 Β· 6,478,100 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee33e337ee0e1f1c07aa0e9e2d2e54135cb9f6e579f37caaf92a16fc9bbb9b40
View on Chainz β†—

Height

#338,491

Difficulty

10.122041

Transactions

1

Size

206 B

Version

2

Bits

0a1f3e18

Nonce

50,787

Timestamp

1/1/2014, 11:25:49 AM

Confirmations

6,478,100

Merkle Root

9bb9b167056c6ae4b165c373fe24577171db70ffad2af41a091aaaa610527ea8
Transactions (1)
Coinbase9bb9b167056c6a…1aaaa610527ea8
1 in β†’ 1 out9.7500 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.

1.936 Γ— 10⁹⁡(96-digit number)
19367244911869766488…53619662212329800000
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
1.936 Γ— 10⁹⁡(96-digit number)
19367244911869766488…53619662212329799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.873 Γ— 10⁹⁡(96-digit number)
38734489823739532976…07239324424659599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.746 Γ— 10⁹⁡(96-digit number)
77468979647479065952…14478648849319199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.549 Γ— 10⁹⁢(97-digit number)
15493795929495813190…28957297698638399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.098 Γ— 10⁹⁢(97-digit number)
30987591858991626380…57914595397276799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.197 Γ— 10⁹⁢(97-digit number)
61975183717983252761…15829190794553599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.239 Γ— 10⁹⁷(98-digit number)
12395036743596650552…31658381589107199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.479 Γ— 10⁹⁷(98-digit number)
24790073487193301104…63316763178214399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.958 Γ— 10⁹⁷(98-digit number)
49580146974386602209…26633526356428799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.916 Γ— 10⁹⁷(98-digit number)
99160293948773204418…53267052712857599999
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 338491

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 ee33e337ee0e1f1c07aa0e9e2d2e54135cb9f6e579f37caaf92a16fc9bbb9b40

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 #338,491 on Chainz β†—
Circulating Supply:57,776,852 XPMΒ·at block #6,816,590 Β· updates every 60s
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