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Block #2,683,577

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/29/2018, 10:23:36 PM Β· Difficulty 11.6898 Β· 4,157,951 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c9fef6667a8e8c572a46e5567ab8a78e1078b2a0847c6e01473b1d6c58c12bd1
View on Chainz β†—

Difficulty

11.689778

Transactions

1

Size

200 B

Version

2

Bits

0bb09552

Nonce

527,513,892

Timestamp

5/29/2018, 10:23:36 PM

Confirmations

4,157,951

Merkle Root

e683b57ed9a41478501beb675cb29406438f80fd1e10d28901fb212bf606d06a
Transactions (1)
Coinbasee683b57ed9a414…fb212bf606d06a
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

9.591 Γ— 10⁹⁴(95-digit number)
95912170135161100484…50869858302050896540
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
9.591 Γ— 10⁹⁴(95-digit number)
95912170135161100484…50869858302050896541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.918 Γ— 10⁹⁡(96-digit number)
19182434027032220096…01739716604101793081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.836 Γ— 10⁹⁡(96-digit number)
38364868054064440193…03479433208203586161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.672 Γ— 10⁹⁡(96-digit number)
76729736108128880387…06958866416407172321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.534 Γ— 10⁹⁢(97-digit number)
15345947221625776077…13917732832814344641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.069 Γ— 10⁹⁢(97-digit number)
30691894443251552154…27835465665628689281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.138 Γ— 10⁹⁢(97-digit number)
61383788886503104309…55670931331257378561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.227 Γ— 10⁹⁷(98-digit number)
12276757777300620861…11341862662514757121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.455 Γ— 10⁹⁷(98-digit number)
24553515554601241723…22683725325029514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.910 Γ— 10⁹⁷(98-digit number)
49107031109202483447…45367450650059028481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.821 Γ— 10⁹⁷(98-digit number)
98214062218404966895…90734901300118056961
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 2683577

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 c9fef6667a8e8c572a46e5567ab8a78e1078b2a0847c6e01473b1d6c58c12bd1

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 #2,683,577 on Chainz β†—
Circulating Supply:57,976,606 XPMΒ·at block #6,841,527 Β· updates every 60s
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