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Home/Chain Registry/Block #3,505,819

Block #3,505,819

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/8/2020, 9:39:47 PM Β· Difficulty 10.9304 Β· 3,339,261 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d520c9d6572a81b768e6db6b70d68ed9b24bd7079029e41fd932cc5d3e4d464
View on Chainz β†—

Difficulty

10.930392

Transactions

1

Size

199 B

Version

2

Bits

0aee2e32

Nonce

833,662,275

Timestamp

1/8/2020, 9:39:47 PM

Confirmations

3,339,261

Merkle Root

2b1167cdf05d25cd66111384e4ff1a342a1b83b976dac1220feaf243e52f6fdd
Transactions (1)
Coinbase2b1167cdf05d25…eaf243e52f6fdd
1 in β†’ 1 out8.3600 XPM109 B
AXfJqzUb…HXeXmjMz
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.

5.740 Γ— 10⁹³(94-digit number)
57401236199239965044…93868510385681568520
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
5.740 Γ— 10⁹³(94-digit number)
57401236199239965044…93868510385681568519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁴(95-digit number)
11480247239847993008…87737020771363137039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.296 Γ— 10⁹⁴(95-digit number)
22960494479695986017…75474041542726274079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.592 Γ— 10⁹⁴(95-digit number)
45920988959391972035…50948083085452548159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.184 Γ— 10⁹⁴(95-digit number)
91841977918783944070…01896166170905096319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.836 Γ— 10⁹⁡(96-digit number)
18368395583756788814…03792332341810192639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.673 Γ— 10⁹⁡(96-digit number)
36736791167513577628…07584664683620385279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.347 Γ— 10⁹⁡(96-digit number)
73473582335027155256…15169329367240770559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.469 Γ— 10⁹⁢(97-digit number)
14694716467005431051…30338658734481541119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.938 Γ— 10⁹⁢(97-digit number)
29389432934010862102…60677317468963082239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.877 Γ— 10⁹⁢(97-digit number)
58778865868021724205…21354634937926164479
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 3505819

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 8d520c9d6572a81b768e6db6b70d68ed9b24bd7079029e41fd932cc5d3e4d464

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 #3,505,819 on Chainz β†—
Circulating Supply:58,005,066 XPMΒ·at block #6,845,079 Β· updates every 60s
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