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Home/Chain Registry/Block #2,126,473

Block #2,126,473

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/21/2017, 6:48:24 AM Β· Difficulty 10.9193 Β· 4,706,568 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5cdc5c248d9fa8df0e3ca2aca07cb731ffba778926d2d434863a6b3dd4ba73e1
View on Chainz β†—

Difficulty

10.919257

Transactions

1

Size

243 B

Version

2

Bits

0aeb546e

Nonce

276,950,684

Timestamp

5/21/2017, 6:48:24 AM

Confirmations

4,706,568

Merkle Root

782e1ccfa42813883bf3e161cfb545966884ce1f0e8453ff41e02239bf38758a
Transactions (1)
Coinbase782e1ccfa42813…e02239bf38758a
1 in β†’ 2 out8.3700 XPM152 B
AS57Lptt…gktTBHgtAXbk7f7A…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.

1.334 Γ— 10⁹⁷(98-digit number)
13347737188214765594…99906677425013248000
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
1.334 Γ— 10⁹⁷(98-digit number)
13347737188214765594…99906677425013247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.669 Γ— 10⁹⁷(98-digit number)
26695474376429531189…99813354850026495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.339 Γ— 10⁹⁷(98-digit number)
53390948752859062378…99626709700052991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁸(99-digit number)
10678189750571812475…99253419400105983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.135 Γ— 10⁹⁸(99-digit number)
21356379501143624951…98506838800211967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.271 Γ— 10⁹⁸(99-digit number)
42712759002287249902…97013677600423935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.542 Γ— 10⁹⁸(99-digit number)
85425518004574499805…94027355200847871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.708 Γ— 10⁹⁹(100-digit number)
17085103600914899961…88054710401695743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.417 Γ— 10⁹⁹(100-digit number)
34170207201829799922…76109420803391487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.834 Γ— 10⁹⁹(100-digit number)
68340414403659599844…52218841606782975999
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 2126473

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 5cdc5c248d9fa8df0e3ca2aca07cb731ffba778926d2d434863a6b3dd4ba73e1

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 #2,126,473 on Chainz β†—
Circulating Supply:57,908,506 XPMΒ·at block #6,833,040 Β· updates every 60s
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