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Home/Chain Registry/Block #2,121,528

Block #2,121,528

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 1:55:45 AM Β· Difficulty 10.9136 Β· 4,714,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1472f6d94325166cf929b9b27aa870baa1c35495de23eae747b6f17690a8f44a
View on Chainz β†—

Difficulty

10.913602

Transactions

1

Size

201 B

Version

2

Bits

0ae9e1ca

Nonce

425,780,959

Timestamp

5/18/2017, 1:55:45 AM

Confirmations

4,714,876

Merkle Root

1ff35c288c202e2e709c06479f3858df60bffe5deae5195526201a6de7cf306b
Transactions (1)
Coinbase1ff35c288c202e…201a6de7cf306b
1 in β†’ 1 out8.3800 XPM110 B
ATysJ82C…iGDyedaR
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.

1.494 Γ— 10⁹⁢(97-digit number)
14942835106495003572…55291343266207252480
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
1.494 Γ— 10⁹⁢(97-digit number)
14942835106495003572…55291343266207252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.988 Γ— 10⁹⁢(97-digit number)
29885670212990007145…10582686532414504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.977 Γ— 10⁹⁢(97-digit number)
59771340425980014290…21165373064829009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.195 Γ— 10⁹⁷(98-digit number)
11954268085196002858…42330746129658019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.390 Γ— 10⁹⁷(98-digit number)
23908536170392005716…84661492259316039681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.781 Γ— 10⁹⁷(98-digit number)
47817072340784011432…69322984518632079361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.563 Γ— 10⁹⁷(98-digit number)
95634144681568022864…38645969037264158721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.912 Γ— 10⁹⁸(99-digit number)
19126828936313604572…77291938074528317441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.825 Γ— 10⁹⁸(99-digit number)
38253657872627209145…54583876149056634881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.650 Γ— 10⁹⁸(99-digit number)
76507315745254418291…09167752298113269761
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 2121528

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 1472f6d94325166cf929b9b27aa870baa1c35495de23eae747b6f17690a8f44a

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 #2,121,528 on Chainz β†—
Circulating Supply:57,935,496 XPMΒ·at block #6,836,403 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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