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Home/Chain Registry/Block #2,853,023

Block #2,853,023

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/24/2018, 8:00:31 AM Β· Difficulty 11.7178 Β· 3,989,668 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c700af90249a642e5ecddb23b4f17fa8c6e79918f1e4d6260c7d08bb197a18dd
View on Chainz β†—

Difficulty

11.717841

Transactions

1

Size

201 B

Version

2

Bits

0bb7c466

Nonce

157,268,193

Timestamp

9/24/2018, 8:00:31 AM

Confirmations

3,989,668

Merkle Root

bd9f835b1f1d837dd7fef216a29313e6cd2828e98142ab6cf873ba47c6734960
Transactions (1)
Coinbasebd9f835b1f1d83…73ba47c6734960
1 in β†’ 1 out7.2700 XPM110 B
AYnEKzDv…LncMzS4H
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.

1.053 Γ— 10⁹⁢(97-digit number)
10530112972966385042…98858344400701713120
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
1.053 Γ— 10⁹⁢(97-digit number)
10530112972966385042…98858344400701713119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.106 Γ— 10⁹⁢(97-digit number)
21060225945932770085…97716688801403426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.212 Γ— 10⁹⁢(97-digit number)
42120451891865540171…95433377602806852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.424 Γ— 10⁹⁢(97-digit number)
84240903783731080343…90866755205613704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.684 Γ— 10⁹⁷(98-digit number)
16848180756746216068…81733510411227409919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.369 Γ— 10⁹⁷(98-digit number)
33696361513492432137…63467020822454819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.739 Γ— 10⁹⁷(98-digit number)
67392723026984864274…26934041644909639679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.347 Γ— 10⁹⁸(99-digit number)
13478544605396972854…53868083289819279359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.695 Γ— 10⁹⁸(99-digit number)
26957089210793945709…07736166579638558719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.391 Γ— 10⁹⁸(99-digit number)
53914178421587891419…15472333159277117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁹(100-digit number)
10782835684317578283…30944666318554234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.156 Γ— 10⁹⁹(100-digit number)
21565671368635156567…61889332637108469759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2853023

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 c700af90249a642e5ecddb23b4f17fa8c6e79918f1e4d6260c7d08bb197a18dd

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 #2,853,023 on Chainz β†—
Circulating Supply:57,985,876 XPMΒ·at block #6,842,690 Β· updates every 60s
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