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Block #66,411

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 5:18:02 PM Β· Difficulty 8.9861 Β· 6,729,318 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cfb64626db22e96c8fdf9c2c54f4b9af38142660ce20c7b9bfdc9c7a92fe9948
View on Chainz β†—

Height

#66,411

Difficulty

8.986133

Transactions

1

Size

203 B

Version

2

Bits

08fc732e

Nonce

60

Timestamp

7/19/2013, 5:18:02 PM

Confirmations

6,729,318

Merkle Root

e2a98cfd752e67c9c9ea90bce253b91ca6eccace788f2627f18309e571eb63c2
Transactions (1)
Coinbasee2a98cfd752e67…8309e571eb63c2
1 in β†’ 1 out12.3700 XPM110 B
AXSFye4r…ADf1YWCU
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.

4.596 Γ— 10¹⁰¹(102-digit number)
45968757238667337641…67726720357457525310
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
4.596 Γ— 10¹⁰¹(102-digit number)
45968757238667337641…67726720357457525311
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.193 Γ— 10¹⁰¹(102-digit number)
91937514477334675283…35453440714915050621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.838 Γ— 10¹⁰²(103-digit number)
18387502895466935056…70906881429830101241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.677 Γ— 10¹⁰²(103-digit number)
36775005790933870113…41813762859660202481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.355 Γ— 10¹⁰²(103-digit number)
73550011581867740226…83627525719320404961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.471 Γ— 10¹⁰³(104-digit number)
14710002316373548045…67255051438640809921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.942 Γ— 10¹⁰³(104-digit number)
29420004632747096090…34510102877281619841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.884 Γ— 10¹⁰³(104-digit number)
58840009265494192181…69020205754563239681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 66411

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 cfb64626db22e96c8fdf9c2c54f4b9af38142660ce20c7b9bfdc9c7a92fe9948

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 #66,411 on Chainz β†—
Circulating Supply:57,609,907 XPMΒ·at block #6,795,728 Β· updates every 60s
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