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Home/Chain Registry/Block #125,982

Block #125,982

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 2:29:00 PM Β· Difficulty 9.7789 Β· 6,674,220 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ccf40c2e7cbbbe39b22c9819cf91918c3910cce3863e88c6239f4adc8b84439
View on Chainz β†—

Height

#125,982

Difficulty

9.778917

Transactions

1

Size

201 B

Version

2

Bits

09c7671c

Nonce

284,761

Timestamp

8/20/2013, 2:29:00 PM

Confirmations

6,674,220

Merkle Root

14d75ee7b4e112c8716af222b8b19a8283775097c2fea34c6463666a952f3aba
Transactions (1)
Coinbase14d75ee7b4e112…63666a952f3aba
1 in β†’ 1 out10.4400 XPM109 B
AN9xPr3q…CZEedeL3
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.

1.140 Γ— 10¹⁰⁰(101-digit number)
11408171058656961234…17100655640521510190
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
1.140 Γ— 10¹⁰⁰(101-digit number)
11408171058656961234…17100655640521510191
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.281 Γ— 10¹⁰⁰(101-digit number)
22816342117313922468…34201311281043020381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.563 Γ— 10¹⁰⁰(101-digit number)
45632684234627844937…68402622562086040761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.126 Γ— 10¹⁰⁰(101-digit number)
91265368469255689875…36805245124172081521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.825 Γ— 10¹⁰¹(102-digit number)
18253073693851137975…73610490248344163041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.650 Γ— 10¹⁰¹(102-digit number)
36506147387702275950…47220980496688326081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.301 Γ— 10¹⁰¹(102-digit number)
73012294775404551900…94441960993376652161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.460 Γ— 10¹⁰²(103-digit number)
14602458955080910380…88883921986753304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.920 Γ— 10¹⁰²(103-digit number)
29204917910161820760…77767843973506608641
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 125982

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 7ccf40c2e7cbbbe39b22c9819cf91918c3910cce3863e88c6239f4adc8b84439

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 #125,982 on Chainz β†—
Circulating Supply:57,645,686 XPMΒ·at block #6,800,201 Β· updates every 60s
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