XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #32,783

Block #32,783

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 3:31:13 AM Β· Difficulty 7.9909 Β· 6,793,377 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
86d53575b956d80b157949599eea88475f486d27d9420441f3900a3c03425889
View on Chainz β†—

Height

#32,783

Difficulty

7.990943

Transactions

1

Size

204 B

Version

2

Bits

07fdae79

Nonce

23

Timestamp

7/14/2013, 3:31:13 AM

Confirmations

6,793,377

Merkle Root

ab4ff8edbb2d8e1845ffed4eba75e60d71df64d947661baa12da1eb53ef90f84
Transactions (1)
Coinbaseab4ff8edbb2d8e…da1eb53ef90f84
1 in β†’ 1 out15.6400 XPM110 B
AQmvEDXt…1BYA7VRt
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.

2.086 Γ— 10¹⁰⁡(106-digit number)
20863884476929906105…37140159858669587440
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
2.086 Γ— 10¹⁰⁡(106-digit number)
20863884476929906105…37140159858669587441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.172 Γ— 10¹⁰⁡(106-digit number)
41727768953859812210…74280319717339174881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.345 Γ— 10¹⁰⁡(106-digit number)
83455537907719624420…48560639434678349761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.669 Γ— 10¹⁰⁢(107-digit number)
16691107581543924884…97121278869356699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.338 Γ— 10¹⁰⁢(107-digit number)
33382215163087849768…94242557738713399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.676 Γ— 10¹⁰⁢(107-digit number)
66764430326175699536…88485115477426798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.335 Γ— 10¹⁰⁷(108-digit number)
13352886065235139907…76970230954853596161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.670 Γ— 10¹⁰⁷(108-digit number)
26705772130470279814…53940461909707192321
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 32783

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 86d53575b956d80b157949599eea88475f486d27d9420441f3900a3c03425889

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 #32,783 on Chainz β†—
Circulating Supply:57,853,407 XPMΒ·at block #6,826,159 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy