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Home/Chain Registry/Block #2,047,643

Block #2,047,643

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/1/2017, 4:46:24 AM Β· Difficulty 10.6871 Β· 4,794,334 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8becb431b5dbe28592b3ae09b0e1cdedca9e9bb31476d406546e93c3d4ac1660
View on Chainz β†—

Difficulty

10.687086

Transactions

1

Size

201 B

Version

2

Bits

0aafe4e4

Nonce

553,406,286

Timestamp

4/1/2017, 4:46:24 AM

Confirmations

4,794,334

Merkle Root

041e49a28357a445f9ba65ea6c7d8fc0da22e2983c5a0458ad8f815d8474baff
Transactions (1)
Coinbase041e49a28357a4…8f815d8474baff
1 in β†’ 1 out8.7400 XPM110 B
AGdmpgf7…fbA3Hbid
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.

2.093 Γ— 10⁹⁢(97-digit number)
20938839123318286442…31720658446059845120
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
2.093 Γ— 10⁹⁢(97-digit number)
20938839123318286442…31720658446059845119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.187 Γ— 10⁹⁢(97-digit number)
41877678246636572885…63441316892119690239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.375 Γ— 10⁹⁢(97-digit number)
83755356493273145770…26882633784239380479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.675 Γ— 10⁹⁷(98-digit number)
16751071298654629154…53765267568478760959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.350 Γ— 10⁹⁷(98-digit number)
33502142597309258308…07530535136957521919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.700 Γ— 10⁹⁷(98-digit number)
67004285194618516616…15061070273915043839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.340 Γ— 10⁹⁸(99-digit number)
13400857038923703323…30122140547830087679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.680 Γ— 10⁹⁸(99-digit number)
26801714077847406646…60244281095660175359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.360 Γ— 10⁹⁸(99-digit number)
53603428155694813293…20488562191320350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.072 Γ— 10⁹⁹(100-digit number)
10720685631138962658…40977124382640701439
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 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
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 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 2047643

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 8becb431b5dbe28592b3ae09b0e1cdedca9e9bb31476d406546e93c3d4ac1660

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 #2,047,643 on Chainz β†—
Circulating Supply:57,980,201 XPMΒ·at block #6,841,976 Β· updates every 60s
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