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Block #145,586

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/1/2013, 11:59:20 PM Β· Difficulty 9.8445 Β· 6,679,830 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
481452b8365df166a12c1854e44ec95c33de7aa598f99e22e267d0a31fa1588d
View on Chainz β†—

Height

#145,586

Difficulty

9.844462

Transactions

2

Size

835 B

Version

2

Bits

09d82eaf

Nonce

4,396

Timestamp

9/1/2013, 11:59:20 PM

Confirmations

6,679,830

Merkle Root

6c114f3de5631b039ad085c77e2c4d321a582801649a81610f96549aceb2b9ec
Transactions (2)
Coinbase31c3ca9e092670…9d1167224dcc06
1 in β†’ 1 out10.3100 XPM109 B
AQaLJ7vK…uZ54Q9BY
12ecdc3cc99ce4…5c719b23479e3e
4 in β†’ 2 out11.2000 XPM635 B
AGBhp4JM…6rdzJgtkAFz9fXym…wh4UqpkL
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.

1.467 Γ— 10⁹⁷(98-digit number)
14676819551869483285…72362977388574787760
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
1.467 Γ— 10⁹⁷(98-digit number)
14676819551869483285…72362977388574787761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.935 Γ— 10⁹⁷(98-digit number)
29353639103738966571…44725954777149575521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.870 Γ— 10⁹⁷(98-digit number)
58707278207477933143…89451909554299151041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.174 Γ— 10⁹⁸(99-digit number)
11741455641495586628…78903819108598302081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.348 Γ— 10⁹⁸(99-digit number)
23482911282991173257…57807638217196604161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.696 Γ— 10⁹⁸(99-digit number)
46965822565982346514…15615276434393208321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.393 Γ— 10⁹⁸(99-digit number)
93931645131964693028…31230552868786416641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.878 Γ— 10⁹⁹(100-digit number)
18786329026392938605…62461105737572833281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.757 Γ— 10⁹⁹(100-digit number)
37572658052785877211…24922211475145666561
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 145586

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 481452b8365df166a12c1854e44ec95c33de7aa598f99e22e267d0a31fa1588d

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 #145,586 on Chainz β†—
Circulating Supply:57,847,429 XPMΒ·at block #6,825,415 Β· updates every 60s
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