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Home/Chain Registry/Block #3,085,463

Block #3,085,463

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2019, 1:42:45 PM Β· Difficulty 11.0310 Β· 3,755,268 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
629d20ad8e167b9ebf4a6821d71cc42194d7d3ffe818ec9bc4c4dc9e4845cf8f
View on Chainz β†—

Difficulty

11.030966

Transactions

1

Size

200 B

Version

2

Bits

0b07ed68

Nonce

520,261,884

Timestamp

3/9/2019, 1:42:45 PM

Confirmations

3,755,268

Merkle Root

826cbb17f240cc061abfad9b406f665fdf51b0ac311198b7f252bfafb60dba57
Transactions (1)
Coinbase826cbb17f240cc…52bfafb60dba57
1 in β†’ 1 out8.2000 XPM109 B
AUMQRepm…tAfKmdW1
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.

2.519 Γ— 10⁹⁷(98-digit number)
25197074327294250172…70091497500963143680
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
2.519 Γ— 10⁹⁷(98-digit number)
25197074327294250172…70091497500963143679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.039 Γ— 10⁹⁷(98-digit number)
50394148654588500345…40182995001926287359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁸(99-digit number)
10078829730917700069…80365990003852574719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.015 Γ— 10⁹⁸(99-digit number)
20157659461835400138…60731980007705149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.031 Γ— 10⁹⁸(99-digit number)
40315318923670800276…21463960015410298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.063 Γ— 10⁹⁸(99-digit number)
80630637847341600553…42927920030820597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁹(100-digit number)
16126127569468320110…85855840061641195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.225 Γ— 10⁹⁹(100-digit number)
32252255138936640221…71711680123282391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.450 Γ— 10⁹⁹(100-digit number)
64504510277873280442…43423360246564782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.290 Γ— 10¹⁰⁰(101-digit number)
12900902055574656088…86846720493129564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.580 Γ— 10¹⁰⁰(101-digit number)
25801804111149312177…73693440986259128319
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 3085463

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 629d20ad8e167b9ebf4a6821d71cc42194d7d3ffe818ec9bc4c4dc9e4845cf8f

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 #3,085,463 on Chainz β†—
Circulating Supply:57,970,192 XPMΒ·at block #6,840,730 Β· updates every 60s
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