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Home/Chain Registry/Block #3,007,535

Block #3,007,535

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2019, 7:00:38 AM Β· Difficulty 11.2069 Β· 3,831,111 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
43ee0a5e4169b6fd29f7e6e4c64e515713ab09eae9c3d37a164d26fe8ec5ada7
View on Chainz β†—

Difficulty

11.206948

Transactions

1

Size

199 B

Version

2

Bits

0b34fa89

Nonce

169,668,592

Timestamp

1/13/2019, 7:00:38 AM

Confirmations

3,831,111

Merkle Root

620ba836367ffa92fc7dc4121510f1b0677d137efcf11a4a920b557b00f61d9d
Transactions (1)
Coinbase620ba836367ffa…0b557b00f61d9d
1 in β†’ 1 out7.9500 XPM110 B
AbXwmGxD…4XXYP765
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.

2.016 Γ— 10⁹²(93-digit number)
20164730451829758683…43515800468242191360
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
2.016 Γ— 10⁹²(93-digit number)
20164730451829758683…43515800468242191359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.032 Γ— 10⁹²(93-digit number)
40329460903659517367…87031600936484382719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.065 Γ— 10⁹²(93-digit number)
80658921807319034734…74063201872968765439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.613 Γ— 10⁹³(94-digit number)
16131784361463806946…48126403745937530879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.226 Γ— 10⁹³(94-digit number)
32263568722927613893…96252807491875061759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.452 Γ— 10⁹³(94-digit number)
64527137445855227787…92505614983750123519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.290 Γ— 10⁹⁴(95-digit number)
12905427489171045557…85011229967500247039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.581 Γ— 10⁹⁴(95-digit number)
25810854978342091114…70022459935000494079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.162 Γ— 10⁹⁴(95-digit number)
51621709956684182229…40044919870000988159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁡(96-digit number)
10324341991336836445…80089839740001976319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.064 Γ— 10⁹⁡(96-digit number)
20648683982673672891…60179679480003952639
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 3007535

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 43ee0a5e4169b6fd29f7e6e4c64e515713ab09eae9c3d37a164d26fe8ec5ada7

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 #3,007,535 on Chainz β†—
Circulating Supply:57,953,433 XPMΒ·at block #6,838,645 Β· updates every 60s
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