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Block #144,434

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/1/2013, 7:43:29 AM Β· Difficulty 9.8389 Β· 6,655,541 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
157aafa725ffac73e0191c0bfffd2d181d3b831d136fd08f0a92f4786da334cc
View on Chainz β†—

Height

#144,434

Difficulty

9.838905

Transactions

2

Size

1.14 KB

Version

2

Bits

09d6c280

Nonce

260,183

Timestamp

9/1/2013, 7:43:29 AM

Confirmations

6,655,541

Merkle Root

96110c1434c29f9430674bd63c6416e4003c47862e3ab0e15dec55b82721a2d1
Transactions (2)
Coinbase530fd073e77388…86505dea9e1c4b
1 in β†’ 1 out10.3300 XPM109 B
AdcZsTmn…W8T9Ht6R
aba239529265e7…96515ec498535c
6 in β†’ 2 out2.0105 XPM967 B
AVtj9fEt…5iKvQNA1AQFT5puj…GUwtUWtR
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.

3.505 Γ— 10⁹⁴(95-digit number)
35057110930931175734…47491540389844992960
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
3.505 Γ— 10⁹⁴(95-digit number)
35057110930931175734…47491540389844992961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.011 Γ— 10⁹⁴(95-digit number)
70114221861862351469…94983080779689985921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.402 Γ— 10⁹⁡(96-digit number)
14022844372372470293…89966161559379971841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.804 Γ— 10⁹⁡(96-digit number)
28045688744744940587…79932323118759943681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.609 Γ— 10⁹⁡(96-digit number)
56091377489489881175…59864646237519887361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.121 Γ— 10⁹⁢(97-digit number)
11218275497897976235…19729292475039774721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.243 Γ— 10⁹⁢(97-digit number)
22436550995795952470…39458584950079549441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.487 Γ— 10⁹⁢(97-digit number)
44873101991591904940…78917169900159098881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.974 Γ— 10⁹⁢(97-digit number)
89746203983183809880…57834339800318197761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 144434

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 157aafa725ffac73e0191c0bfffd2d181d3b831d136fd08f0a92f4786da334cc

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 #144,434 on Chainz β†—
Circulating Supply:57,643,860 XPMΒ·at block #6,799,974 Β· updates every 60s
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