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Home/Chain Registry/Block #2,129,366

Block #2,129,366

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2017, 3:48:28 PM Β· Difficulty 10.9105 Β· 4,715,029 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
92431b4561ea0129ba442553582fbd65dde49e793d9d65222a1e956f5eae279f
View on Chainz β†—

Difficulty

10.910473

Transactions

1

Size

200 B

Version

2

Bits

0ae914c4

Nonce

619,091,535

Timestamp

5/23/2017, 3:48:28 PM

Confirmations

4,715,029

Merkle Root

db78d6d409eaaa682706c0a9af8070c636584faf5f367c5d4b25d6ace63d88b0
Transactions (1)
Coinbasedb78d6d409eaaa…25d6ace63d88b0
1 in β†’ 1 out8.3900 XPM110 B
AJwWJHqw…vRw6ST2e
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.

5.705 Γ— 10⁹³(94-digit number)
57053140907076701621…46814855290558737580
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
5.705 Γ— 10⁹³(94-digit number)
57053140907076701621…46814855290558737581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.141 Γ— 10⁹⁴(95-digit number)
11410628181415340324…93629710581117475161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.282 Γ— 10⁹⁴(95-digit number)
22821256362830680648…87259421162234950321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.564 Γ— 10⁹⁴(95-digit number)
45642512725661361296…74518842324469900641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.128 Γ— 10⁹⁴(95-digit number)
91285025451322722593…49037684648939801281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.825 Γ— 10⁹⁡(96-digit number)
18257005090264544518…98075369297879602561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.651 Γ— 10⁹⁡(96-digit number)
36514010180529089037…96150738595759205121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.302 Γ— 10⁹⁡(96-digit number)
73028020361058178074…92301477191518410241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.460 Γ— 10⁹⁢(97-digit number)
14605604072211635614…84602954383036820481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.921 Γ— 10⁹⁢(97-digit number)
29211208144423271229…69205908766073640961
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 2129366

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 92431b4561ea0129ba442553582fbd65dde49e793d9d65222a1e956f5eae279f

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 #2,129,366 on Chainz β†—
Circulating Supply:57,999,551 XPMΒ·at block #6,844,394 Β· updates every 60s
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