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Block #106,407

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2013, 12:37:31 AM Β· Difficulty 9.6051 Β· 6,718,173 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fcaa391fefa29026680f2869fcd8cf8a51ca77a5ba72cabad8d52be912980465
View on Chainz β†—

Height

#106,407

Difficulty

9.605135

Transactions

1

Size

199 B

Version

2

Bits

099aea22

Nonce

59,267

Timestamp

8/9/2013, 12:37:31 AM

Confirmations

6,718,173

Merkle Root

b7a8e3d9bdc4f24ce664fa61174868495926487d2a2393e9d34ae439fcae4476
Transactions (1)
Coinbaseb7a8e3d9bdc4f2…4ae439fcae4476
1 in β†’ 1 out10.8200 XPM109 B
AWCd5D8d…B4W6Mbxa
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.

1.031 Γ— 10⁹⁡(96-digit number)
10310846094152575396…16222779429988976000
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
1.031 Γ— 10⁹⁡(96-digit number)
10310846094152575396…16222779429988976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.062 Γ— 10⁹⁡(96-digit number)
20621692188305150792…32445558859977952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.124 Γ— 10⁹⁡(96-digit number)
41243384376610301584…64891117719955904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.248 Γ— 10⁹⁡(96-digit number)
82486768753220603168…29782235439911808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.649 Γ— 10⁹⁢(97-digit number)
16497353750644120633…59564470879823616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.299 Γ— 10⁹⁢(97-digit number)
32994707501288241267…19128941759647232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.598 Γ— 10⁹⁢(97-digit number)
65989415002576482534…38257883519294464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.319 Γ— 10⁹⁷(98-digit number)
13197883000515296506…76515767038588928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.639 Γ— 10⁹⁷(98-digit number)
26395766001030593013…53031534077177856001
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 106407

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 fcaa391fefa29026680f2869fcd8cf8a51ca77a5ba72cabad8d52be912980465

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 #106,407 on Chainz β†—
Circulating Supply:57,840,707 XPMΒ·at block #6,824,579 Β· updates every 60s
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