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Block #145,641

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2013, 12:48:18 AM Β· Difficulty 9.8446 Β· 6,655,370 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f1e2b5cd4fba1361f9b822ced3eae05111f8d58455deedcce162bb3514c4215
View on Chainz β†—

Height

#145,641

Difficulty

9.844648

Transactions

2

Size

1.14 KB

Version

2

Bits

09d83ad3

Nonce

122,788

Timestamp

9/2/2013, 12:48:18 AM

Confirmations

6,655,370

Merkle Root

c63954d6d5992d07b50588126917cf03c114d9c37e8e515f73bca491b2f3a182
Transactions (2)
Coinbaseea4a2a4113a34f…e5a5a61bf0b499
1 in β†’ 1 out10.3200 XPM109 B
AKid32nG…AENo7UoT
c3e4e08c988737…6a0da97627ad89
6 in β†’ 2 out97.7641 XPM965 B
AVmdBeTf…bqxiUsyrAWeWcPM1…BA2a8s16
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.

1.499 Γ— 10⁹⁡(96-digit number)
14998073153293049333…47314008965505551460
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
1.499 Γ— 10⁹⁡(96-digit number)
14998073153293049333…47314008965505551461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.999 Γ— 10⁹⁡(96-digit number)
29996146306586098666…94628017931011102921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.999 Γ— 10⁹⁡(96-digit number)
59992292613172197333…89256035862022205841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.199 Γ— 10⁹⁢(97-digit number)
11998458522634439466…78512071724044411681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.399 Γ— 10⁹⁢(97-digit number)
23996917045268878933…57024143448088823361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.799 Γ— 10⁹⁢(97-digit number)
47993834090537757867…14048286896177646721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.598 Γ— 10⁹⁢(97-digit number)
95987668181075515734…28096573792355293441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.919 Γ— 10⁹⁷(98-digit number)
19197533636215103146…56193147584710586881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.839 Γ— 10⁹⁷(98-digit number)
38395067272430206293…12386295169421173761
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 145641

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 3f1e2b5cd4fba1361f9b822ced3eae05111f8d58455deedcce162bb3514c4215

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 #145,641 on Chainz β†—
Circulating Supply:57,652,149 XPMΒ·at block #6,801,010 Β· updates every 60s
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