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Block #2,645,360

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 9:07:43 PM Β· Difficulty 11.7309 Β· 4,186,669 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6c1714a4c65316df7d503221d854d0963d5753c365f2ab38ea4c960542481d23
View on Chainz β†—

Difficulty

11.730853

Transactions

1

Size

200 B

Version

2

Bits

0bbb192f

Nonce

1,209,203,467

Timestamp

5/2/2018, 9:07:43 PM

Confirmations

4,186,669

Merkle Root

b72a69aa34a24af3f3dd187c2e3ee0c6310c3fd811d5505dc5c2ef728a896b92
Transactions (1)
Coinbaseb72a69aa34a24a…c2ef728a896b92
1 in β†’ 1 out7.2500 XPM110 B
AWdZqj5K…vVoE9UUP
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.

8.711 Γ— 10⁹⁡(96-digit number)
87118241053056302101…59009413116398008320
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
8.711 Γ— 10⁹⁡(96-digit number)
87118241053056302101…59009413116398008319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.742 Γ— 10⁹⁢(97-digit number)
17423648210611260420…18018826232796016639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.484 Γ— 10⁹⁢(97-digit number)
34847296421222520840…36037652465592033279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.969 Γ— 10⁹⁢(97-digit number)
69694592842445041681…72075304931184066559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁷(98-digit number)
13938918568489008336…44150609862368133119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.787 Γ— 10⁹⁷(98-digit number)
27877837136978016672…88301219724736266239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.575 Γ— 10⁹⁷(98-digit number)
55755674273956033344…76602439449472532479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁸(99-digit number)
11151134854791206668…53204878898945064959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.230 Γ— 10⁹⁸(99-digit number)
22302269709582413337…06409757797890129919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.460 Γ— 10⁹⁸(99-digit number)
44604539419164826675…12819515595780259839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.920 Γ— 10⁹⁸(99-digit number)
89209078838329653351…25639031191560519679
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 2645360

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 6c1714a4c65316df7d503221d854d0963d5753c365f2ab38ea4c960542481d23

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 #2,645,360 on Chainz β†—
Circulating Supply:57,900,364 XPMΒ·at block #6,832,028 Β· updates every 60s
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