XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #347,551

Block #347,551

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/7/2014, 7:00:53 AM Β· Difficulty 10.2361 Β· 6,452,813 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0f10a8fa3e5418b7bb7eeaf348a82fe5065b5f8cebd2c4b91383960fdd6ab769
View on Chainz β†—

Height

#347,551

Difficulty

10.236123

Transactions

1

Size

201 B

Version

2

Bits

0a3c7290

Nonce

56,023

Timestamp

1/7/2014, 7:00:53 AM

Confirmations

6,452,813

Merkle Root

c8c2430c6eac02eb53235be32d338ac58f05d412a471f860331ac268670f202e
Transactions (1)
Coinbasec8c2430c6eac02…1ac268670f202e
1 in β†’ 1 out9.5300 XPM109 B
AJLpU7nU…CnB9CeBg
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.

1.461 Γ— 10¹⁰⁰(101-digit number)
14613544810498007656…48666630485794156800
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
1.461 Γ— 10¹⁰⁰(101-digit number)
14613544810498007656…48666630485794156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.922 Γ— 10¹⁰⁰(101-digit number)
29227089620996015312…97333260971588313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.845 Γ— 10¹⁰⁰(101-digit number)
58454179241992030625…94666521943176627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.169 Γ— 10¹⁰¹(102-digit number)
11690835848398406125…89333043886353254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.338 Γ— 10¹⁰¹(102-digit number)
23381671696796812250…78666087772706508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.676 Γ— 10¹⁰¹(102-digit number)
46763343393593624500…57332175545413017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.352 Γ— 10¹⁰¹(102-digit number)
93526686787187249001…14664351090826035201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.870 Γ— 10¹⁰²(103-digit number)
18705337357437449800…29328702181652070401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.741 Γ— 10¹⁰²(103-digit number)
37410674714874899600…58657404363304140801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.482 Γ— 10¹⁰²(103-digit number)
74821349429749799201…17314808726608281601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.496 Γ— 10¹⁰³(104-digit number)
14964269885949959840…34629617453216563201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 347551

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 0f10a8fa3e5418b7bb7eeaf348a82fe5065b5f8cebd2c4b91383960fdd6ab769

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 #347,551 on Chainz β†—
Circulating Supply:57,646,971 XPMΒ·at block #6,800,363 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