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Home/Chain Registry/Block #3,003,952

Block #3,003,952

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/10/2019, 7:10:55 PM Β· Difficulty 11.2079 Β· 3,839,089 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c95eaa0cec13b76bb388bc80b988db86d0649b4f4c8c8b5c3a19274596b3aaca
View on Chainz β†—

Difficulty

11.207886

Transactions

2

Size

574 B

Version

2

Bits

0b353808

Nonce

1,578,563,181

Timestamp

1/10/2019, 7:10:55 PM

Confirmations

3,839,089

Merkle Root

ec040550698102321311e0ac776aad4d01a945158f1cea60bbdd54841a00235a
Transactions (2)
Coinbase93085b8b985ac4…18bb47af18f223
1 in β†’ 1 out7.9600 XPM110 B
AbXwmGxD…4XXYP765
35d313802033e0…49f5325496ed38
2 in β†’ 2 out5.5394 XPM374 B
Ac46JApH…3bgULjJCAUhjokok…k5m93PZR
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.

4.242 Γ— 10⁹⁡(96-digit number)
42426195371516067570…70504782205289976800
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
4.242 Γ— 10⁹⁡(96-digit number)
42426195371516067570…70504782205289976799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.485 Γ— 10⁹⁡(96-digit number)
84852390743032135140…41009564410579953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.697 Γ— 10⁹⁢(97-digit number)
16970478148606427028…82019128821159907199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.394 Γ— 10⁹⁢(97-digit number)
33940956297212854056…64038257642319814399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.788 Γ— 10⁹⁢(97-digit number)
67881912594425708112…28076515284639628799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.357 Γ— 10⁹⁷(98-digit number)
13576382518885141622…56153030569279257599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.715 Γ— 10⁹⁷(98-digit number)
27152765037770283245…12306061138558515199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.430 Γ— 10⁹⁷(98-digit number)
54305530075540566490…24612122277117030399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.086 Γ— 10⁹⁸(99-digit number)
10861106015108113298…49224244554234060799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.172 Γ— 10⁹⁸(99-digit number)
21722212030216226596…98448489108468121599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.344 Γ— 10⁹⁸(99-digit number)
43444424060432453192…96896978216936243199
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 3003952

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 c95eaa0cec13b76bb388bc80b988db86d0649b4f4c8c8b5c3a19274596b3aaca

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 #3,003,952 on Chainz β†—
Circulating Supply:57,988,685 XPMΒ·at block #6,843,040 Β· updates every 60s
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