XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #332,020

Block #332,020

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/27/2013, 6:07:10 PM Β· Difficulty 10.1749 Β· 6,468,854 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31d2d23205b2769e2f6a8f7d2971a8457558add20e2d984a3d3aa759aa460ef4
View on Chainz β†—

Height

#332,020

Difficulty

10.174901

Transactions

1

Size

208 B

Version

2

Bits

0a2cc64e

Nonce

157,648

Timestamp

12/27/2013, 6:07:10 PM

Confirmations

6,468,854

Merkle Root

2da102bfc4471d74b61e339b503602a9cf2d48b79af4225ba370c32e64bd0816
Transactions (1)
Coinbase2da102bfc4471d…70c32e64bd0816
1 in β†’ 1 out9.6400 XPM116 B
AbwWkWZt…kawDhufa
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.

9.752 Γ— 10⁹⁸(99-digit number)
97527270685573545771…38554222598605838400
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.752 Γ— 10⁹⁸(99-digit number)
97527270685573545771…38554222598605838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.950 Γ— 10⁹⁹(100-digit number)
19505454137114709154…77108445197211676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.901 Γ— 10⁹⁹(100-digit number)
39010908274229418308…54216890394423353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.802 Γ— 10⁹⁹(100-digit number)
78021816548458836616…08433780788846707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.560 Γ— 10¹⁰⁰(101-digit number)
15604363309691767323…16867561577693414399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.120 Γ— 10¹⁰⁰(101-digit number)
31208726619383534646…33735123155386828799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.241 Γ— 10¹⁰⁰(101-digit number)
62417453238767069293…67470246310773657599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.248 Γ— 10¹⁰¹(102-digit number)
12483490647753413858…34940492621547315199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.496 Γ— 10¹⁰¹(102-digit number)
24966981295506827717…69880985243094630399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.993 Γ— 10¹⁰¹(102-digit number)
49933962591013655434…39761970486189260799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 332020

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 31d2d23205b2769e2f6a8f7d2971a8457558add20e2d984a3d3aa759aa460ef4

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 #332,020 on Chainz β†—
Circulating Supply:57,651,049 XPMΒ·at block #6,800,873 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