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Block #2,809,088

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/25/2018, 9:16:17 AM Β· Difficulty 11.6669 Β· 4,032,789 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be8b68658da5ad487a6b93e0f2e599462f1725d5fcd7e482d1a1beb6b22ee7ca
View on Chainz β†—

Difficulty

11.666941

Transactions

1

Size

201 B

Version

2

Bits

0baabcab

Nonce

377,650,467

Timestamp

8/25/2018, 9:16:17 AM

Confirmations

4,032,789

Merkle Root

d31402f7fa8693ee4179203c069a4237f8720cfdd46e276452923485123716e3
Transactions (1)
Coinbased31402f7fa8693…923485123716e3
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.866 Γ— 10⁹⁢(97-digit number)
18661964334738342982…06369606586513981440
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
1.866 Γ— 10⁹⁢(97-digit number)
18661964334738342982…06369606586513981439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.732 Γ— 10⁹⁢(97-digit number)
37323928669476685964…12739213173027962879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.464 Γ— 10⁹⁢(97-digit number)
74647857338953371929…25478426346055925759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁷(98-digit number)
14929571467790674385…50956852692111851519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.985 Γ— 10⁹⁷(98-digit number)
29859142935581348771…01913705384223703039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.971 Γ— 10⁹⁷(98-digit number)
59718285871162697543…03827410768447406079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.194 Γ— 10⁹⁸(99-digit number)
11943657174232539508…07654821536894812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.388 Γ— 10⁹⁸(99-digit number)
23887314348465079017…15309643073789624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.777 Γ— 10⁹⁸(99-digit number)
47774628696930158034…30619286147579248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.554 Γ— 10⁹⁸(99-digit number)
95549257393860316069…61238572295158497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.910 Γ— 10⁹⁹(100-digit number)
19109851478772063213…22477144590316994559
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 2809088

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 be8b68658da5ad487a6b93e0f2e599462f1725d5fcd7e482d1a1beb6b22ee7ca

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 #2,809,088 on Chainz β†—
Circulating Supply:57,979,392 XPMΒ·at block #6,841,876 Β· updates every 60s
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