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Home/Chain Registry/Block #2,167,505

Block #2,167,505

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/19/2017, 3:03:34 PM Β· Difficulty 10.8984 Β· 4,675,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06c651c61af4a24d4ef64ff7a1cb997bc2cfa8c94608e1755cc9c22b267c66e0
View on Chainz β†—

Difficulty

10.898392

Transactions

1

Size

200 B

Version

2

Bits

0ae5fd07

Nonce

18,840,293

Timestamp

6/19/2017, 3:03:34 PM

Confirmations

4,675,850

Merkle Root

d06ee33a0b1c493a9dcad93d7baa88ba2009f5a3318764dc0b60beb5dff57295
Transactions (1)
Coinbased06ee33a0b1c49…60beb5dff57295
1 in β†’ 1 out8.4100 XPM110 B
APye9AHP…MfaSuSSM
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.

1.961 Γ— 10⁹⁡(96-digit number)
19611389134425957966…96202777178409288040
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
1.961 Γ— 10⁹⁡(96-digit number)
19611389134425957966…96202777178409288041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.922 Γ— 10⁹⁡(96-digit number)
39222778268851915933…92405554356818576081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.844 Γ— 10⁹⁡(96-digit number)
78445556537703831866…84811108713637152161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.568 Γ— 10⁹⁢(97-digit number)
15689111307540766373…69622217427274304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.137 Γ— 10⁹⁢(97-digit number)
31378222615081532746…39244434854548608641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.275 Γ— 10⁹⁢(97-digit number)
62756445230163065492…78488869709097217281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.255 Γ— 10⁹⁷(98-digit number)
12551289046032613098…56977739418194434561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.510 Γ— 10⁹⁷(98-digit number)
25102578092065226197…13955478836388869121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.020 Γ— 10⁹⁷(98-digit number)
50205156184130452394…27910957672777738241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.004 Γ— 10⁹⁸(99-digit number)
10041031236826090478…55821915345555476481
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 2167505

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 06c651c61af4a24d4ef64ff7a1cb997bc2cfa8c94608e1755cc9c22b267c66e0

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 #2,167,505 on Chainz β†—
Circulating Supply:57,991,202 XPMΒ·at block #6,843,354 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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