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Block #2,268,514

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2017, 7:24:44 AM Β· Difficulty 10.9525 Β· 4,576,459 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7691360b0c65757e83d4b385659bcdda773a847863fab9c5e0c53b5a62f4882c
View on Chainz β†—

Difficulty

10.952492

Transactions

1

Size

243 B

Version

2

Bits

0af3d68b

Nonce

2,433,846,874

Timestamp

8/26/2017, 7:24:44 AM

Confirmations

4,576,459

Merkle Root

db82fa6fb042fe1bf26642a65ead8ad7d0fbe69537d8ba4b8428a89e026a6dce
Transactions (1)
Coinbasedb82fa6fb042fe…28a89e026a6dce
1 in β†’ 2 out8.3200 XPM152 B
ARNe3C8D…KfGUT8YNAXbk7f7A…Tx7JECPG
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.

2.206 Γ— 10⁹⁷(98-digit number)
22067307005764057522…54120344306866304000
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
2.206 Γ— 10⁹⁷(98-digit number)
22067307005764057522…54120344306866303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.413 Γ— 10⁹⁷(98-digit number)
44134614011528115045…08240688613732607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.826 Γ— 10⁹⁷(98-digit number)
88269228023056230091…16481377227465215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.765 Γ— 10⁹⁸(99-digit number)
17653845604611246018…32962754454930431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.530 Γ— 10⁹⁸(99-digit number)
35307691209222492036…65925508909860863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.061 Γ— 10⁹⁸(99-digit number)
70615382418444984072…31851017819721727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.412 Γ— 10⁹⁹(100-digit number)
14123076483688996814…63702035639443455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.824 Γ— 10⁹⁹(100-digit number)
28246152967377993629…27404071278886911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.649 Γ— 10⁹⁹(100-digit number)
56492305934755987258…54808142557773823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.129 Γ— 10¹⁰⁰(101-digit number)
11298461186951197451…09616285115547647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.259 Γ— 10¹⁰⁰(101-digit number)
22596922373902394903…19232570231095295999
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 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
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 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 2268514

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 7691360b0c65757e83d4b385659bcdda773a847863fab9c5e0c53b5a62f4882c

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 #2,268,514 on Chainz β†—
Circulating Supply:58,004,202 XPMΒ·at block #6,844,972 Β· updates every 60s
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