XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #58,272

Block #58,272

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 7:47:24 PM Β· Difficulty 8.9590 Β· 6,768,419 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5eddc3566c3fe43b50ce52bb51deb4c06e652086418b5e5cc8e39ac89fd8f9a2
View on Chainz β†—

Height

#58,272

Difficulty

8.958991

Transactions

1

Size

199 B

Version

2

Bits

08f58068

Nonce

393

Timestamp

7/17/2013, 7:47:24 PM

Confirmations

6,768,419

Merkle Root

bf676afeeecc45d271c4fe57550668d8ec07a4eea3571a3623b2322478f53310
Transactions (1)
Coinbasebf676afeeecc45…b2322478f53310
1 in β†’ 1 out12.4400 XPM109 B
APnz4kGc…qXozup97
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.

7.318 Γ— 10⁹³(94-digit number)
73181979850473629151…25374637667360089090
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
7.318 Γ— 10⁹³(94-digit number)
73181979850473629151…25374637667360089091
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.463 Γ— 10⁹⁴(95-digit number)
14636395970094725830…50749275334720178181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.927 Γ— 10⁹⁴(95-digit number)
29272791940189451660…01498550669440356361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.854 Γ— 10⁹⁴(95-digit number)
58545583880378903321…02997101338880712721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.170 Γ— 10⁹⁡(96-digit number)
11709116776075780664…05994202677761425441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.341 Γ— 10⁹⁡(96-digit number)
23418233552151561328…11988405355522850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.683 Γ— 10⁹⁡(96-digit number)
46836467104303122657…23976810711045701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.367 Γ— 10⁹⁡(96-digit number)
93672934208606245314…47953621422091403521
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 58272

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 5eddc3566c3fe43b50ce52bb51deb4c06e652086418b5e5cc8e39ac89fd8f9a2

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 #58,272 on Chainz β†—
Circulating Supply:57,857,679 XPMΒ·at block #6,826,690 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