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Block #126,529

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 10:32:40 PM Β· Difficulty 9.7817 Β· 6,700,513 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
485c9417ec2b28381b540a36a7700097266af11b6347f88c277e09c4394b80a7
View on Chainz β†—

Height

#126,529

Difficulty

9.781703

Transactions

2

Size

359 B

Version

2

Bits

09c81db3

Nonce

406,262

Timestamp

8/20/2013, 10:32:40 PM

Confirmations

6,700,513

Merkle Root

8a1402a2da7ddfab455db89d2939e78285037493e7078818253d2d9358c8b2d6
Transactions (2)
Coinbase2edeff59692c43…625c66f4f22eab
1 in β†’ 1 out10.4500 XPM109 B
AdQaxQix…1Po7rnqY
374427a1afa4fc…1d8da715981dec
1 in β†’ 1 out10.5300 XPM159 B
AaiQ25kC…uarGkYVE
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.

3.410 Γ— 10⁹⁢(97-digit number)
34108485503940580731…30906934036681250740
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
3.410 Γ— 10⁹⁢(97-digit number)
34108485503940580731…30906934036681250741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.821 Γ— 10⁹⁢(97-digit number)
68216971007881161462…61813868073362501481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.364 Γ— 10⁹⁷(98-digit number)
13643394201576232292…23627736146725002961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.728 Γ— 10⁹⁷(98-digit number)
27286788403152464585…47255472293450005921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.457 Γ— 10⁹⁷(98-digit number)
54573576806304929170…94510944586900011841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.091 Γ— 10⁹⁸(99-digit number)
10914715361260985834…89021889173800023681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.182 Γ— 10⁹⁸(99-digit number)
21829430722521971668…78043778347600047361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.365 Γ— 10⁹⁸(99-digit number)
43658861445043943336…56087556695200094721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.731 Γ— 10⁹⁸(99-digit number)
87317722890087886672…12175113390400189441
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 126529

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 485c9417ec2b28381b540a36a7700097266af11b6347f88c277e09c4394b80a7

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 #126,529 on Chainz β†—
Circulating Supply:57,860,516 XPMΒ·at block #6,827,041 Β· updates every 60s
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