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Home/Chain Registry/Block #1,780,952

Block #1,780,952

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2016, 8:05:18 PM Β· Difficulty 10.7651 Β· 5,060,092 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
18456a056ca965a49ae6c1a27ed869f7e0d3c862155194e0d3857589d4756e68
View on Chainz β†—

Difficulty

10.765075

Transactions

2

Size

1016 B

Version

2

Bits

0ac3dbee

Nonce

1,073,028,915

Timestamp

9/26/2016, 8:05:18 PM

Confirmations

5,060,092

Merkle Root

de6af32c957563d5aed7afcd2ae04198388b21873ea2fa939ec222d372296f79
Transactions (2)
Coinbase158c2b57cc98b9…61bf489357924f
1 in β†’ 1 out8.6300 XPM109 B
AVv5ZTm5…T9So4bXH
3fac183385fbe4…7b1c60e7913388
5 in β†’ 2 out86.3813 XPM816 B
AJgJk7rB…vqaUgp3yAdeJVddG…2Kc9MJ4n
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.

1.211 Γ— 10⁹⁢(97-digit number)
12112839147621658608…35513703941239713280
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
1.211 Γ— 10⁹⁢(97-digit number)
12112839147621658608…35513703941239713281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.422 Γ— 10⁹⁢(97-digit number)
24225678295243317216…71027407882479426561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.845 Γ— 10⁹⁢(97-digit number)
48451356590486634433…42054815764958853121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.690 Γ— 10⁹⁢(97-digit number)
96902713180973268867…84109631529917706241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.938 Γ— 10⁹⁷(98-digit number)
19380542636194653773…68219263059835412481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.876 Γ— 10⁹⁷(98-digit number)
38761085272389307547…36438526119670824961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.752 Γ— 10⁹⁷(98-digit number)
77522170544778615094…72877052239341649921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.550 Γ— 10⁹⁸(99-digit number)
15504434108955723018…45754104478683299841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.100 Γ— 10⁹⁸(99-digit number)
31008868217911446037…91508208957366599681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.201 Γ— 10⁹⁸(99-digit number)
62017736435822892075…83016417914733199361
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 1780952

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 18456a056ca965a49ae6c1a27ed869f7e0d3c862155194e0d3857589d4756e68

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 #1,780,952 on Chainz β†—
Circulating Supply:57,972,713 XPMΒ·at block #6,841,043 Β· updates every 60s
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