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Home/Chain Registry/Block #1,682,107

Block #1,682,107

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 6:50:21 PM Β· Difficulty 10.7185 Β· 5,150,040 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aa2c0c84e90653ba4118b1ecf46bd990682f981f43006528211b4a6211fbe22f
View on Chainz β†—

Difficulty

10.718534

Transactions

1

Size

243 B

Version

2

Bits

0ab7f1d4

Nonce

1,719,559,774

Timestamp

7/20/2016, 6:50:21 PM

Confirmations

5,150,040

Merkle Root

5e1f0decf34c8ba487b99a829c13a90dd0911289814f0bb79ce7bc4a7730e7d3
Transactions (1)
Coinbase5e1f0decf34c8b…e7bc4a7730e7d3
1 in β†’ 2 out8.6900 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…EJXLjVFh
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.

8.894 Γ— 10⁹⁡(96-digit number)
88945987020319785319…43497926381553804560
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
8.894 Γ— 10⁹⁡(96-digit number)
88945987020319785319…43497926381553804561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.778 Γ— 10⁹⁢(97-digit number)
17789197404063957063…86995852763107609121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.557 Γ— 10⁹⁢(97-digit number)
35578394808127914127…73991705526215218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.115 Γ— 10⁹⁢(97-digit number)
71156789616255828255…47983411052430436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.423 Γ— 10⁹⁷(98-digit number)
14231357923251165651…95966822104860872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.846 Γ— 10⁹⁷(98-digit number)
28462715846502331302…91933644209721745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.692 Γ— 10⁹⁷(98-digit number)
56925431693004662604…83867288419443491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.138 Γ— 10⁹⁸(99-digit number)
11385086338600932520…67734576838886983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.277 Γ— 10⁹⁸(99-digit number)
22770172677201865041…35469153677773967361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.554 Γ— 10⁹⁸(99-digit number)
45540345354403730083…70938307355547934721
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 1682107

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 aa2c0c84e90653ba4118b1ecf46bd990682f981f43006528211b4a6211fbe22f

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 #1,682,107 on Chainz β†—
Circulating Supply:57,901,313 XPMΒ·at block #6,832,146 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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