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Block #853,605

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/15/2014, 12:23:32 AM Β· Difficulty 10.9689 Β· 5,991,409 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3208eace8863fd112a2c41c6539c4b38fee8085b908f97d9d21abf052af02f97
View on Chainz β†—

Height

#853,605

Difficulty

10.968930

Transactions

2

Size

399 B

Version

2

Bits

0af80bc5

Nonce

589,695,458

Timestamp

12/15/2014, 12:23:32 AM

Confirmations

5,991,409

Merkle Root

b136d7936a9e42437d32b7fe7d886d7137d5b319f65f96798223f16c0b659529
Transactions (2)
Coinbase2b267f2de76458…96398d67702ae4
1 in β†’ 1 out8.3190 XPM116 B
ANSXnLY2…Sd25TjkD
9264c0357ad90b…e68fb3a34cdcdd
1 in β†’ 1 out0.0104 XPM192 B
AJaaDqHL…JjX8Ha7z
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.

8.867 Γ— 10⁹⁢(97-digit number)
88679246082796997449…03227304274802416640
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
8.867 Γ— 10⁹⁢(97-digit number)
88679246082796997449…03227304274802416639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.773 Γ— 10⁹⁷(98-digit number)
17735849216559399489…06454608549604833279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.547 Γ— 10⁹⁷(98-digit number)
35471698433118798979…12909217099209666559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.094 Γ— 10⁹⁷(98-digit number)
70943396866237597959…25818434198419333119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.418 Γ— 10⁹⁸(99-digit number)
14188679373247519591…51636868396838666239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.837 Γ— 10⁹⁸(99-digit number)
28377358746495039183…03273736793677332479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.675 Γ— 10⁹⁸(99-digit number)
56754717492990078367…06547473587354664959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.135 Γ— 10⁹⁹(100-digit number)
11350943498598015673…13094947174709329919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.270 Γ— 10⁹⁹(100-digit number)
22701886997196031347…26189894349418659839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.540 Γ— 10⁹⁹(100-digit number)
45403773994392062694…52379788698837319679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.080 Γ— 10⁹⁹(100-digit number)
90807547988784125388…04759577397674639359
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 853605

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 3208eace8863fd112a2c41c6539c4b38fee8085b908f97d9d21abf052af02f97

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 #853,605 on Chainz β†—
Circulating Supply:58,004,534 XPMΒ·at block #6,845,013 Β· updates every 60s
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