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Block #289,360

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2013, 4:15:58 AM Β· Difficulty 9.9885 Β· 6,537,617 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b9eb5f57e5c7b8ae69b6480d8636474f0a36afa53240385bd23e8ea8a53f9b43
View on Chainz β†—

Height

#289,360

Difficulty

9.988467

Transactions

1

Size

208 B

Version

2

Bits

09fd0c2c

Nonce

518,249

Timestamp

12/2/2013, 4:15:58 AM

Confirmations

6,537,617

Merkle Root

9c5ccfd0c3d6c62f7556fcdbe1d3c3251d30a8a6064d1125f923f9ddd10f7c05
Transactions (1)
Coinbase9c5ccfd0c3d6c6…23f9ddd10f7c05
1 in β†’ 1 out10.0100 XPM116 B
AcLBm5Z9…S683d7c3
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.

7.357 Γ— 10⁹⁸(99-digit number)
73573191411288530256…99717271207707331200
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
7.357 Γ— 10⁹⁸(99-digit number)
73573191411288530256…99717271207707331201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.471 Γ— 10⁹⁹(100-digit number)
14714638282257706051…99434542415414662401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.942 Γ— 10⁹⁹(100-digit number)
29429276564515412102…98869084830829324801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.885 Γ— 10⁹⁹(100-digit number)
58858553129030824204…97738169661658649601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.177 Γ— 10¹⁰⁰(101-digit number)
11771710625806164840…95476339323317299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.354 Γ— 10¹⁰⁰(101-digit number)
23543421251612329681…90952678646634598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.708 Γ— 10¹⁰⁰(101-digit number)
47086842503224659363…81905357293269196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.417 Γ— 10¹⁰⁰(101-digit number)
94173685006449318727…63810714586538393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.883 Γ— 10¹⁰¹(102-digit number)
18834737001289863745…27621429173076787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.766 Γ— 10¹⁰¹(102-digit number)
37669474002579727491…55242858346153574401
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 289360

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 b9eb5f57e5c7b8ae69b6480d8636474f0a36afa53240385bd23e8ea8a53f9b43

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 #289,360 on Chainz β†—
Circulating Supply:57,859,991 XPMΒ·at block #6,826,976 Β· updates every 60s
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