XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #353,248

Block #353,248

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2014, 8:02:55 PM Β· Difficulty 10.3226 Β· 6,441,629 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
52b23fff1d514b9808ed757ec6bde03370718d167866ec46ced8fcdbb36960f9
View on Chainz β†—

Height

#353,248

Difficulty

10.322581

Transactions

1

Size

210 B

Version

2

Bits

0a5294aa

Nonce

13,686

Timestamp

1/10/2014, 8:02:55 PM

Confirmations

6,441,629

Merkle Root

d797ce8de2c11e8f338d3fdc1ea84749c1405d2ccbfbeaded19a5a31b477f1ae
Transactions (1)
Coinbased797ce8de2c11e…9a5a31b477f1ae
1 in β†’ 1 out9.3700 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.

1.596 Γ— 10¹⁰⁴(105-digit number)
15965692139797596649…86824498233307299840
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
1.596 Γ— 10¹⁰⁴(105-digit number)
15965692139797596649…86824498233307299841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.193 Γ— 10¹⁰⁴(105-digit number)
31931384279595193299…73648996466614599681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.386 Γ— 10¹⁰⁴(105-digit number)
63862768559190386598…47297992933229199361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.277 Γ— 10¹⁰⁡(106-digit number)
12772553711838077319…94595985866458398721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.554 Γ— 10¹⁰⁡(106-digit number)
25545107423676154639…89191971732916797441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.109 Γ— 10¹⁰⁡(106-digit number)
51090214847352309278…78383943465833594881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.021 Γ— 10¹⁰⁢(107-digit number)
10218042969470461855…56767886931667189761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.043 Γ— 10¹⁰⁢(107-digit number)
20436085938940923711…13535773863334379521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.087 Γ— 10¹⁰⁢(107-digit number)
40872171877881847423…27071547726668759041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.174 Γ— 10¹⁰⁢(107-digit number)
81744343755763694846…54143095453337518081
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 353248

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 52b23fff1d514b9808ed757ec6bde03370718d167866ec46ced8fcdbb36960f9

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 #353,248 on Chainz β†—
Circulating Supply:57,603,050 XPMΒ·at block #6,794,876 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