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Block #364,602

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/18/2014, 4:45:05 AM Β· Difficulty 10.4206 Β· 6,450,311 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bfcadcb5f0fd6cc922f1085a53ee7ae2a00ac35e37f8d236c832ab0327df015
View on Chainz β†—

Height

#364,602

Difficulty

10.420588

Transactions

1

Size

212 B

Version

2

Bits

0a6babb0

Nonce

1,090,221

Timestamp

1/18/2014, 4:45:05 AM

Confirmations

6,450,311

Merkle Root

f17dfc2d7e72ae546c130f4842f6a4a05ff1422a4da5768692a502f1ed8041d2
Transactions (1)
Coinbasef17dfc2d7e72ae…a502f1ed8041d2
1 in β†’ 1 out9.1900 XPM118 B
AW6FdqAF…mbtgXE2r
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.

2.170 Γ— 10¹⁰³(104-digit number)
21706552607342040566…36458617219653304320
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
2.170 Γ— 10¹⁰³(104-digit number)
21706552607342040566…36458617219653304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.341 Γ— 10¹⁰³(104-digit number)
43413105214684081133…72917234439306608641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.682 Γ— 10¹⁰³(104-digit number)
86826210429368162267…45834468878613217281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.736 Γ— 10¹⁰⁴(105-digit number)
17365242085873632453…91668937757226434561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.473 Γ— 10¹⁰⁴(105-digit number)
34730484171747264907…83337875514452869121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.946 Γ— 10¹⁰⁴(105-digit number)
69460968343494529814…66675751028905738241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.389 Γ— 10¹⁰⁡(106-digit number)
13892193668698905962…33351502057811476481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.778 Γ— 10¹⁰⁡(106-digit number)
27784387337397811925…66703004115622952961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.556 Γ— 10¹⁰⁡(106-digit number)
55568774674795623851…33406008231245905921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.111 Γ— 10¹⁰⁢(107-digit number)
11113754934959124770…66812016462491811841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 364602

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 6bfcadcb5f0fd6cc922f1085a53ee7ae2a00ac35e37f8d236c832ab0327df015

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 #364,602 on Chainz β†—
Circulating Supply:57,763,396 XPMΒ·at block #6,814,912 Β· updates every 60s
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