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Home/Chain Registry/Block #2,666,472

Block #2,666,472

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2018, 7:05:18 AM Β· Difficulty 11.6670 Β· 4,176,400 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d51883fd897145c0f0ee4eee8387ba85f2ecd04493f29f108f3f75c0144c27f1
View on Chainz β†—

Difficulty

11.667029

Transactions

1

Size

200 B

Version

2

Bits

0baac26c

Nonce

94,812,884

Timestamp

5/18/2018, 7:05:18 AM

Confirmations

4,176,400

Merkle Root

f27fb34593a28fb68adffadcf6c5345b8774f4116c79158de4e3c008fae993b0
Transactions (1)
Coinbasef27fb34593a28f…e3c008fae993b0
1 in β†’ 1 out7.3300 XPM110 B
ASStUkio…cf3dDfZZ
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.

2.510 Γ— 10⁹⁴(95-digit number)
25102311078885048986…37240643655777602920
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.510 Γ— 10⁹⁴(95-digit number)
25102311078885048986…37240643655777602921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.020 Γ— 10⁹⁴(95-digit number)
50204622157770097973…74481287311555205841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.004 Γ— 10⁹⁡(96-digit number)
10040924431554019594…48962574623110411681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.008 Γ— 10⁹⁡(96-digit number)
20081848863108039189…97925149246220823361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.016 Γ— 10⁹⁡(96-digit number)
40163697726216078378…95850298492441646721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.032 Γ— 10⁹⁡(96-digit number)
80327395452432156756…91700596984883293441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.606 Γ— 10⁹⁢(97-digit number)
16065479090486431351…83401193969766586881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.213 Γ— 10⁹⁢(97-digit number)
32130958180972862702…66802387939533173761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.426 Γ— 10⁹⁢(97-digit number)
64261916361945725405…33604775879066347521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.285 Γ— 10⁹⁷(98-digit number)
12852383272389145081…67209551758132695041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.570 Γ— 10⁹⁷(98-digit number)
25704766544778290162…34419103516265390081
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2666472

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 d51883fd897145c0f0ee4eee8387ba85f2ecd04493f29f108f3f75c0144c27f1

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 #2,666,472 on Chainz β†—
Circulating Supply:57,987,320 XPMΒ·at block #6,842,871 Β· updates every 60s
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