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Block #148,940

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 1:28:12 AM Β· Difficulty 9.8561 Β· 6,667,023 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0ac3c002c0a94d153a4ac1d4d0d2470ad1d067c7024910f4c9d12126dffaf93b
View on Chainz β†—

Height

#148,940

Difficulty

9.856109

Transactions

1

Size

198 B

Version

2

Bits

09db29f0

Nonce

48,497

Timestamp

9/4/2013, 1:28:12 AM

Confirmations

6,667,023

Merkle Root

c255a1b43867ce4037a1c685b35ca860bf4f549a94fc7aff90b9055ff8d9c884
Transactions (1)
Coinbasec255a1b43867ce…b9055ff8d9c884
1 in β†’ 1 out10.2800 XPM109 B
ASki8pmA…Dwetzr7b
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.

7.414 Γ— 10⁹¹(92-digit number)
74141375922391099814…09152008110401054720
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
7.414 Γ— 10⁹¹(92-digit number)
74141375922391099814…09152008110401054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.482 Γ— 10⁹²(93-digit number)
14828275184478219962…18304016220802109441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.965 Γ— 10⁹²(93-digit number)
29656550368956439925…36608032441604218881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.931 Γ— 10⁹²(93-digit number)
59313100737912879851…73216064883208437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.186 Γ— 10⁹³(94-digit number)
11862620147582575970…46432129766416875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.372 Γ— 10⁹³(94-digit number)
23725240295165151940…92864259532833751041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.745 Γ— 10⁹³(94-digit number)
47450480590330303881…85728519065667502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.490 Γ— 10⁹³(94-digit number)
94900961180660607762…71457038131335004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.898 Γ— 10⁹⁴(95-digit number)
18980192236132121552…42914076262670008321
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 148940

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 0ac3c002c0a94d153a4ac1d4d0d2470ad1d067c7024910f4c9d12126dffaf93b

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 #148,940 on Chainz β†—
Circulating Supply:57,771,819 XPMΒ·at block #6,815,962 Β· updates every 60s
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