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Block #283,094

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/29/2013, 2:59:39 PM Β· Difficulty 9.9804 Β· 6,559,044 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e58f76ddb0896906f23ad99cdc375c6a4a23c3aa4b593ad1ab496bf777f5e81
View on Chainz β†—

Height

#283,094

Difficulty

9.980450

Transactions

1

Size

207 B

Version

2

Bits

09fafec4

Nonce

3,155

Timestamp

11/29/2013, 2:59:39 PM

Confirmations

6,559,044

Merkle Root

95bed47c0b9911f7c09dba2fb83dca1ce8ea95783c7145a9bdd2725811a05221
Transactions (1)
Coinbase95bed47c0b9911…d2725811a05221
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.161 Γ— 10⁹⁢(97-digit number)
41617964398209584831…26981434881735797760
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
4.161 Γ— 10⁹⁢(97-digit number)
41617964398209584831…26981434881735797761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.323 Γ— 10⁹⁢(97-digit number)
83235928796419169663…53962869763471595521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.664 Γ— 10⁹⁷(98-digit number)
16647185759283833932…07925739526943191041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.329 Γ— 10⁹⁷(98-digit number)
33294371518567667865…15851479053886382081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.658 Γ— 10⁹⁷(98-digit number)
66588743037135335730…31702958107772764161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.331 Γ— 10⁹⁸(99-digit number)
13317748607427067146…63405916215545528321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.663 Γ— 10⁹⁸(99-digit number)
26635497214854134292…26811832431091056641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.327 Γ— 10⁹⁸(99-digit number)
53270994429708268584…53623664862182113281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.065 Γ— 10⁹⁹(100-digit number)
10654198885941653716…07247329724364226561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.130 Γ— 10⁹⁹(100-digit number)
21308397771883307433…14494659448728453121
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 283094

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 3e58f76ddb0896906f23ad99cdc375c6a4a23c3aa4b593ad1ab496bf777f5e81

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 #283,094 on Chainz β†—
Circulating Supply:57,981,494 XPMΒ·at block #6,842,137 Β· updates every 60s
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