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Block #153,590

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 2:53:30 AM Β· Difficulty 9.8631 Β· 6,672,644 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df3068ab5e48a09942d00315eb20c92b9bb2412b54dfb415cc9317bb5b6897ba
View on Chainz β†—

Height

#153,590

Difficulty

9.863128

Transactions

1

Size

198 B

Version

2

Bits

09dcf5fa

Nonce

213,611

Timestamp

9/7/2013, 2:53:30 AM

Confirmations

6,672,644

Merkle Root

ca8a531478215002a97328f1c08bc772edac866ab757f3e2f735f585fa55f3c4
Transactions (1)
Coinbaseca8a5314782150…35f585fa55f3c4
1 in β†’ 1 out10.2600 XPM109 B
APjQSnMT…gWnyPTW3
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.

5.944 Γ— 10⁹¹(92-digit number)
59448386046886410619…68357125043927915360
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
5.944 Γ— 10⁹¹(92-digit number)
59448386046886410619…68357125043927915361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.188 Γ— 10⁹²(93-digit number)
11889677209377282123…36714250087855830721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.377 Γ— 10⁹²(93-digit number)
23779354418754564247…73428500175711661441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.755 Γ— 10⁹²(93-digit number)
47558708837509128495…46857000351423322881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.511 Γ— 10⁹²(93-digit number)
95117417675018256991…93714000702846645761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.902 Γ— 10⁹³(94-digit number)
19023483535003651398…87428001405693291521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.804 Γ— 10⁹³(94-digit number)
38046967070007302796…74856002811386583041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.609 Γ— 10⁹³(94-digit number)
76093934140014605593…49712005622773166081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.521 Γ— 10⁹⁴(95-digit number)
15218786828002921118…99424011245546332161
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 153590

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 df3068ab5e48a09942d00315eb20c92b9bb2412b54dfb415cc9317bb5b6897ba

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 #153,590 on Chainz β†—
Circulating Supply:57,854,003 XPMΒ·at block #6,826,233 Β· updates every 60s
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