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Home/Chain Registry/Block #2,657,294

Block #2,657,294

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/11/2018, 8:57:40 PM Β· Difficulty 11.6715 Β· 4,185,549 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cce0def91687b5a89e9dbeb1cd4d29f26cfb5630735f857da31381c1a3b7b090
View on Chainz β†—

Difficulty

11.671480

Transactions

1

Size

201 B

Version

2

Bits

0babe624

Nonce

194,654,798

Timestamp

5/11/2018, 8:57:40 PM

Confirmations

4,185,549

Merkle Root

9da9eca6d9999f109a5c1de0bfd2564955a902041391ae984efbcb9183bc7585
Transactions (1)
Coinbase9da9eca6d9999f…fbcb9183bc7585
1 in β†’ 1 out7.3300 XPM110 B
ASzcCrWU…5mLR99kc
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.

8.414 Γ— 10⁹⁢(97-digit number)
84148618041211023865…32003637853597102080
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
8.414 Γ— 10⁹⁢(97-digit number)
84148618041211023865…32003637853597102079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.682 Γ— 10⁹⁷(98-digit number)
16829723608242204773…64007275707194204159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.365 Γ— 10⁹⁷(98-digit number)
33659447216484409546…28014551414388408319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.731 Γ— 10⁹⁷(98-digit number)
67318894432968819092…56029102828776816639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.346 Γ— 10⁹⁸(99-digit number)
13463778886593763818…12058205657553633279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.692 Γ— 10⁹⁸(99-digit number)
26927557773187527636…24116411315107266559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.385 Γ— 10⁹⁸(99-digit number)
53855115546375055273…48232822630214533119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.077 Γ— 10⁹⁹(100-digit number)
10771023109275011054…96465645260429066239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.154 Γ— 10⁹⁹(100-digit number)
21542046218550022109…92931290520858132479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.308 Γ— 10⁹⁹(100-digit number)
43084092437100044219…85862581041716264959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.616 Γ— 10⁹⁹(100-digit number)
86168184874200088438…71725162083432529919
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 2657294

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 cce0def91687b5a89e9dbeb1cd4d29f26cfb5630735f857da31381c1a3b7b090

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 #2,657,294 on Chainz β†—
Circulating Supply:57,987,088 XPMΒ·at block #6,842,842 Β· updates every 60s
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