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Block #149,121

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 4:14:20 AM Β· Difficulty 9.8566 Β· 6,677,893 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0a1456faeac0a417e262601aacf8ce3de11d7ccbc3430788310164700c6938f3
View on Chainz β†—

Height

#149,121

Difficulty

9.856570

Transactions

1

Size

206 B

Version

2

Bits

09db482b

Nonce

33,555,128

Timestamp

9/4/2013, 4:14:20 AM

Confirmations

6,677,893

Merkle Root

669b2d40502a4cae5e4bb6447c6a1689a666d2d67b33d599280a882ecdb7e6e3
Transactions (1)
Coinbase669b2d40502a4c…0a882ecdb7e6e3
1 in β†’ 1 out10.2800 XPM112 B
AT5A2KL6…CT16n6i2
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.

5.947 Γ— 10¹⁰³(104-digit number)
59473613089796100691…33290156915346397120
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
5.947 Γ— 10¹⁰³(104-digit number)
59473613089796100691…33290156915346397121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.189 Γ— 10¹⁰⁴(105-digit number)
11894722617959220138…66580313830692794241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.378 Γ— 10¹⁰⁴(105-digit number)
23789445235918440276…33160627661385588481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.757 Γ— 10¹⁰⁴(105-digit number)
47578890471836880553…66321255322771176961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.515 Γ— 10¹⁰⁴(105-digit number)
95157780943673761106…32642510645542353921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.903 Γ— 10¹⁰⁡(106-digit number)
19031556188734752221…65285021291084707841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.806 Γ— 10¹⁰⁡(106-digit number)
38063112377469504442…30570042582169415681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.612 Γ— 10¹⁰⁡(106-digit number)
76126224754939008885…61140085164338831361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.522 Γ— 10¹⁰⁢(107-digit number)
15225244950987801777…22280170328677662721
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 149121

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 0a1456faeac0a417e262601aacf8ce3de11d7ccbc3430788310164700c6938f3

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 #149,121 on Chainz β†—
Circulating Supply:57,860,289 XPMΒ·at block #6,827,013 Β· updates every 60s
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