XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #426,299

Block #426,299

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/2/2014, 12:40:43 PM Β· Difficulty 10.3626 Β· 6,371,817 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
efeb44c97c6eea08543362515d30461b03416cea4f248e12e6aefe32f6238a22
View on Chainz β†—

Height

#426,299

Difficulty

10.362572

Transactions

2

Size

2.15 KB

Version

2

Bits

0a5cd17f

Nonce

49,371

Timestamp

3/2/2014, 12:40:43 PM

Confirmations

6,371,817

Merkle Root

a58a0a570451537e8f9d56af164c06f3653128acfbe78d91886470b8ab20667c
Transactions (2)
Coinbase83390679857315…46c97d8b063b3c
1 in β†’ 1 out9.3300 XPM109 B
AGAZ2wz6…84mNH2V3
5634893ee5f09f…cef8bc0bfc6df3
13 in β†’ 2 out40.0111 XPM1.95 KB
ARmApX8E…8QYcu7sTALGEm14C…NEsPLwku
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.

2.847 Γ— 10¹⁰³(104-digit number)
28477514783640032455…25813172510440523520
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
2.847 Γ— 10¹⁰³(104-digit number)
28477514783640032455…25813172510440523521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.695 Γ— 10¹⁰³(104-digit number)
56955029567280064910…51626345020881047041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.139 Γ— 10¹⁰⁴(105-digit number)
11391005913456012982…03252690041762094081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.278 Γ— 10¹⁰⁴(105-digit number)
22782011826912025964…06505380083524188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.556 Γ— 10¹⁰⁴(105-digit number)
45564023653824051928…13010760167048376321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.112 Γ— 10¹⁰⁴(105-digit number)
91128047307648103856…26021520334096752641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.822 Γ— 10¹⁰⁡(106-digit number)
18225609461529620771…52043040668193505281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.645 Γ— 10¹⁰⁡(106-digit number)
36451218923059241542…04086081336387010561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.290 Γ— 10¹⁰⁡(106-digit number)
72902437846118483085…08172162672774021121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.458 Γ— 10¹⁰⁢(107-digit number)
14580487569223696617…16344325345548042241
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 426299

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 efeb44c97c6eea08543362515d30461b03416cea4f248e12e6aefe32f6238a22

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 #426,299 on Chainz β†—
Circulating Supply:57,628,930 XPMΒ·at block #6,798,115 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK