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Home/Chain Registry/Block #2,129,124

Block #2,129,124

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/23/2017, 10:49:38 AM Β· Difficulty 10.9114 Β· 4,714,899 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a2ef0819d7b42adedfa6b78b7560895028d91e5f4be33ffd5a2e7b774c7e45a0
View on Chainz β†—

Difficulty

10.911448

Transactions

1

Size

199 B

Version

2

Bits

0ae954aa

Nonce

1,451,699,944

Timestamp

5/23/2017, 10:49:38 AM

Confirmations

4,714,899

Merkle Root

2cd4ae367ee5942f3deccb2771dc9b7b443c551d0a98ef6f4008de4ba8ca5002
Transactions (1)
Coinbase2cd4ae367ee594…08de4ba8ca5002
1 in β†’ 1 out8.3900 XPM109 B
ANTAqsXt…HAt3LGRw
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.

1.168 Γ— 10⁹⁡(96-digit number)
11681563712943895248…70736654594534318080
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.168 Γ— 10⁹⁡(96-digit number)
11681563712943895248…70736654594534318079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.336 Γ— 10⁹⁡(96-digit number)
23363127425887790497…41473309189068636159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.672 Γ— 10⁹⁡(96-digit number)
46726254851775580994…82946618378137272319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.345 Γ— 10⁹⁡(96-digit number)
93452509703551161989…65893236756274544639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁢(97-digit number)
18690501940710232397…31786473512549089279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.738 Γ— 10⁹⁢(97-digit number)
37381003881420464795…63572947025098178559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.476 Γ— 10⁹⁢(97-digit number)
74762007762840929591…27145894050196357119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.495 Γ— 10⁹⁷(98-digit number)
14952401552568185918…54291788100392714239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.990 Γ— 10⁹⁷(98-digit number)
29904803105136371836…08583576200785428479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.980 Γ— 10⁹⁷(98-digit number)
59809606210272743673…17167152401570856959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2129124

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 a2ef0819d7b42adedfa6b78b7560895028d91e5f4be33ffd5a2e7b774c7e45a0

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 #2,129,124 on Chainz β†—
Circulating Supply:57,996,566 XPMΒ·at block #6,844,022 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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