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Block #126,156

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/20/2013, 5:03:35 PM Β· Difficulty 9.7797 Β· 6,678,807 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57cd9fa41a5b5461b66a250691d829e6a0ad4f101e5c8de2bae34f05e1fb1d03
View on Chainz β†—

Height

#126,156

Difficulty

9.779738

Transactions

1

Size

199 B

Version

2

Bits

09c79ce9

Nonce

169,088

Timestamp

8/20/2013, 5:03:35 PM

Confirmations

6,678,807

Merkle Root

51bd20aa5a42c1de52a2eba91825c17cb69064a6e533a6daad976c700baa6c09
Transactions (1)
Coinbase51bd20aa5a42c1…976c700baa6c09
1 in β†’ 1 out10.4400 XPM109 B
AcDnt5if…zE9DMhu8
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.

9.443 Γ— 10⁹⁴(95-digit number)
94434607012191893777…22435045713620820180
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
9.443 Γ— 10⁹⁴(95-digit number)
94434607012191893777…22435045713620820181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.888 Γ— 10⁹⁡(96-digit number)
18886921402438378755…44870091427241640361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.777 Γ— 10⁹⁡(96-digit number)
37773842804876757511…89740182854483280721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.554 Γ— 10⁹⁡(96-digit number)
75547685609753515022…79480365708966561441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.510 Γ— 10⁹⁢(97-digit number)
15109537121950703004…58960731417933122881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.021 Γ— 10⁹⁢(97-digit number)
30219074243901406008…17921462835866245761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.043 Γ— 10⁹⁢(97-digit number)
60438148487802812017…35842925671732491521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.208 Γ— 10⁹⁷(98-digit number)
12087629697560562403…71685851343464983041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.417 Γ— 10⁹⁷(98-digit number)
24175259395121124807…43371702686929966081
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 126156

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 57cd9fa41a5b5461b66a250691d829e6a0ad4f101e5c8de2bae34f05e1fb1d03

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 #126,156 on Chainz β†—
Circulating Supply:57,683,771 XPMΒ·at block #6,804,962 Β· updates every 60s
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