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Block #184,021

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/28/2013, 9:56:21 AM Β· Difficulty 9.8586 Β· 6,617,620 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
88965cf9722177313caf97dde9ef5ea910d36f887d17a5fbdd005cfa80c43ffa
View on Chainz β†—

Height

#184,021

Difficulty

9.858566

Transactions

2

Size

392 B

Version

2

Bits

09dbcafb

Nonce

53,395

Timestamp

9/28/2013, 9:56:21 AM

Confirmations

6,617,620

Merkle Root

65861b8651eaf8ce326879cf44e059a241a581d0afc244d94218f4a80e9fa38b
Transactions (2)
Coinbaseb370e2739c3bc6…269420b5b0ee61
1 in β†’ 1 out10.2800 XPM109 B
AaijpUsJ…KsHAh9oh
f3c511cf3e2a5b…5a89e990d6cd03
1 in β†’ 1 out2.9923 XPM192 B
ASazCFjo…nA3y7k5f
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.

1.580 Γ— 10⁹⁷(98-digit number)
15802222861940305472…65363851730612060160
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
1.580 Γ— 10⁹⁷(98-digit number)
15802222861940305472…65363851730612060161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.160 Γ— 10⁹⁷(98-digit number)
31604445723880610945…30727703461224120321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.320 Γ— 10⁹⁷(98-digit number)
63208891447761221891…61455406922448240641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.264 Γ— 10⁹⁸(99-digit number)
12641778289552244378…22910813844896481281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.528 Γ— 10⁹⁸(99-digit number)
25283556579104488756…45821627689792962561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.056 Γ— 10⁹⁸(99-digit number)
50567113158208977513…91643255379585925121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.011 Γ— 10⁹⁹(100-digit number)
10113422631641795502…83286510759171850241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.022 Γ— 10⁹⁹(100-digit number)
20226845263283591005…66573021518343700481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.045 Γ— 10⁹⁹(100-digit number)
40453690526567182010…33146043036687400961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.090 Γ— 10⁹⁹(100-digit number)
80907381053134364021…66292086073374801921
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 184021

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 88965cf9722177313caf97dde9ef5ea910d36f887d17a5fbdd005cfa80c43ffa

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 #184,021 on Chainz β†—
Circulating Supply:57,657,209 XPMΒ·at block #6,801,640 Β· updates every 60s
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