XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #31,421

Block #31,421

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 11:21:47 PM Β· Difficulty 7.9887 Β· 6,794,788 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fab5bf030505ccbd1ab3c81396c29cb16ec4cce7371d1560b46af258f3894c48
View on Chainz β†—

Height

#31,421

Difficulty

7.988662

Transactions

2

Size

359 B

Version

2

Bits

07fd18ef

Nonce

965

Timestamp

7/13/2013, 11:21:47 PM

Confirmations

6,794,788

Merkle Root

1d6e8a35d0ea0cc2f51e54d261783169e8900fdd49142be04f57af7e0ef78fd9
Transactions (2)
Coinbase0f709ff0a0aa72…6b2cfab856e85b
1 in β†’ 1 out15.6600 XPM109 B
Aa6CvCkU…kRW6ZeWm
4445d7ef8aa2ef…533655c419e7fb
1 in β†’ 1 out15.7100 XPM157 B
AWeWcPM1…BA2a8s16
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.

1.000 Γ— 10¹⁰³(104-digit number)
10003496696439754894…64605806650372898240
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
1.000 Γ— 10¹⁰³(104-digit number)
10003496696439754894…64605806650372898239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.000 Γ— 10¹⁰³(104-digit number)
20006993392879509788…29211613300745796479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.001 Γ— 10¹⁰³(104-digit number)
40013986785759019577…58423226601491592959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.002 Γ— 10¹⁰³(104-digit number)
80027973571518039154…16846453202983185919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.600 Γ— 10¹⁰⁴(105-digit number)
16005594714303607830…33692906405966371839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.201 Γ— 10¹⁰⁴(105-digit number)
32011189428607215661…67385812811932743679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.402 Γ— 10¹⁰⁴(105-digit number)
64022378857214431323…34771625623865487359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.280 Γ— 10¹⁰⁡(106-digit number)
12804475771442886264…69543251247730974719
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 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
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 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 31421

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 fab5bf030505ccbd1ab3c81396c29cb16ec4cce7371d1560b46af258f3894c48

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 #31,421 on Chainz β†—
Circulating Supply:57,853,803 XPMΒ·at block #6,826,208 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