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Block #335,174

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/30/2013, 12:51:59 AM Β· Difficulty 10.1548 Β· 6,460,559 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d1ed1ce867bb32ac5b46460121a5484f200c2cfeb04c9244cfa3b50fcbe196d3
View on Chainz β†—

Height

#335,174

Difficulty

10.154767

Transactions

1

Size

210 B

Version

2

Bits

0a279ecb

Nonce

134,219,406

Timestamp

12/30/2013, 12:51:59 AM

Confirmations

6,460,559

Merkle Root

59a6813198a57fd9a11c5e08a9310a8333bfba55e09c1dff722ad456aee5def1
Transactions (1)
Coinbase59a6813198a57f…2ad456aee5def1
1 in β†’ 1 out9.6800 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.

6.969 Γ— 10¹⁰³(104-digit number)
69696917185207267365…28575769842021922880
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
6.969 Γ— 10¹⁰³(104-digit number)
69696917185207267365…28575769842021922879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.393 Γ— 10¹⁰⁴(105-digit number)
13939383437041453473…57151539684043845759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.787 Γ— 10¹⁰⁴(105-digit number)
27878766874082906946…14303079368087691519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.575 Γ— 10¹⁰⁴(105-digit number)
55757533748165813892…28606158736175383039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.115 Γ— 10¹⁰⁡(106-digit number)
11151506749633162778…57212317472350766079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.230 Γ— 10¹⁰⁡(106-digit number)
22303013499266325556…14424634944701532159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.460 Γ— 10¹⁰⁡(106-digit number)
44606026998532651113…28849269889403064319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.921 Γ— 10¹⁰⁡(106-digit number)
89212053997065302227…57698539778806128639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.784 Γ— 10¹⁰⁢(107-digit number)
17842410799413060445…15397079557612257279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.568 Γ— 10¹⁰⁢(107-digit number)
35684821598826120890…30794159115224514559
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 335174

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 d1ed1ce867bb32ac5b46460121a5484f200c2cfeb04c9244cfa3b50fcbe196d3

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 #335,174 on Chainz β†—
Circulating Supply:57,609,940 XPMΒ·at block #6,795,732 Β· updates every 60s
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