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Home/Chain Registry/Block #1,873,592

Block #1,873,592

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2016, 10:25:01 AM Β· Difficulty 10.6681 Β· 4,964,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3733a8bca2fbf3ee265fcb7eb59c060c51c5eb47106680f55d184620b1d3b149
View on Chainz β†—

Difficulty

10.668079

Transactions

1

Size

198 B

Version

2

Bits

0aab0734

Nonce

505,441,230

Timestamp

12/1/2016, 10:25:01 AM

Confirmations

4,964,850

Merkle Root

7d4139885d743424714fac48b4d715ae5a23534f8cf7ec42d8cab9d1cbddee7f
Transactions (1)
Coinbase7d4139885d7434…cab9d1cbddee7f
1 in β†’ 1 out8.7700 XPM109 B
AYQBHoyt…5C4WCEkf
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.

2.754 Γ— 10⁹²(93-digit number)
27540772293140823909…94988011541370496320
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
2.754 Γ— 10⁹²(93-digit number)
27540772293140823909…94988011541370496321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.508 Γ— 10⁹²(93-digit number)
55081544586281647818…89976023082740992641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.101 Γ— 10⁹³(94-digit number)
11016308917256329563…79952046165481985281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.203 Γ— 10⁹³(94-digit number)
22032617834512659127…59904092330963970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.406 Γ— 10⁹³(94-digit number)
44065235669025318254…19808184661927941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.813 Γ— 10⁹³(94-digit number)
88130471338050636509…39616369323855882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.762 Γ— 10⁹⁴(95-digit number)
17626094267610127301…79232738647711764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.525 Γ— 10⁹⁴(95-digit number)
35252188535220254603…58465477295423528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.050 Γ— 10⁹⁴(95-digit number)
70504377070440509207…16930954590847057921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.410 Γ— 10⁹⁡(96-digit number)
14100875414088101841…33861909181694115841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.820 Γ— 10⁹⁡(96-digit number)
28201750828176203683…67723818363388231681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1873592

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 3733a8bca2fbf3ee265fcb7eb59c060c51c5eb47106680f55d184620b1d3b149

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 #1,873,592 on Chainz β†—
Circulating Supply:57,951,813 XPMΒ·at block #6,838,441 Β· updates every 60s
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