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Home/Chain Registry/Block #2,272,061

Block #2,272,061

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/28/2017, 4:00:31 PM Β· Difficulty 10.9540 Β· 4,569,562 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d4221733fb945dc18ae8d105f910d4201426cb181d53392287423dcb0d89b990
View on Chainz β†—

Difficulty

10.953980

Transactions

1

Size

199 B

Version

2

Bits

0af4380a

Nonce

1,107,512,004

Timestamp

8/28/2017, 4:00:31 PM

Confirmations

4,569,562

Merkle Root

f325ff6f3341956764195d55d4fc55fab16fddb88602b284af759cd0c1750fa9
Transactions (1)
Coinbasef325ff6f334195…759cd0c1750fa9
1 in β†’ 1 out8.3200 XPM110 B
Ad8UJsVB…k786DuLR
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.

1.643 Γ— 10⁹³(94-digit number)
16438902043005512987…13171087749743732240
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
1.643 Γ— 10⁹³(94-digit number)
16438902043005512987…13171087749743732241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.287 Γ— 10⁹³(94-digit number)
32877804086011025974…26342175499487464481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.575 Γ— 10⁹³(94-digit number)
65755608172022051949…52684350998974928961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.315 Γ— 10⁹⁴(95-digit number)
13151121634404410389…05368701997949857921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.630 Γ— 10⁹⁴(95-digit number)
26302243268808820779…10737403995899715841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.260 Γ— 10⁹⁴(95-digit number)
52604486537617641559…21474807991799431681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.052 Γ— 10⁹⁡(96-digit number)
10520897307523528311…42949615983598863361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.104 Γ— 10⁹⁡(96-digit number)
21041794615047056623…85899231967197726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.208 Γ— 10⁹⁡(96-digit number)
42083589230094113247…71798463934395453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.416 Γ— 10⁹⁡(96-digit number)
84167178460188226495…43596927868790906881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2272061

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 d4221733fb945dc18ae8d105f910d4201426cb181d53392287423dcb0d89b990

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 #2,272,061 on Chainz β†—
Circulating Supply:57,977,366 XPMΒ·at block #6,841,622 Β· updates every 60s
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