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Block #289,591

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2013, 7:04:04 AM Β· Difficulty 9.9886 Β· 6,506,890 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
39b810f5d1ff12d9f568938b99f268533e8ced8cd40e16b070303336be43fcce
View on Chainz β†—

Height

#289,591

Difficulty

9.988615

Transactions

1

Size

209 B

Version

2

Bits

09fd15d8

Nonce

16,778,303

Timestamp

12/2/2013, 7:04:04 AM

Confirmations

6,506,890

Merkle Root

c3b543c9b0d40efc264b07497248034181ecd2324b3020f9f28cc15fefe33499
Transactions (1)
Coinbasec3b543c9b0d40e…8cc15fefe33499
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.

1.309 Γ— 10¹⁰¹(102-digit number)
13099678826247349376…50610466279042993280
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
1.309 Γ— 10¹⁰¹(102-digit number)
13099678826247349376…50610466279042993281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.619 Γ— 10¹⁰¹(102-digit number)
26199357652494698753…01220932558085986561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.239 Γ— 10¹⁰¹(102-digit number)
52398715304989397507…02441865116171973121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.047 Γ— 10¹⁰²(103-digit number)
10479743060997879501…04883730232343946241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.095 Γ— 10¹⁰²(103-digit number)
20959486121995759002…09767460464687892481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.191 Γ— 10¹⁰²(103-digit number)
41918972243991518005…19534920929375784961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.383 Γ— 10¹⁰²(103-digit number)
83837944487983036011…39069841858751569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.676 Γ— 10¹⁰³(104-digit number)
16767588897596607202…78139683717503139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.353 Γ— 10¹⁰³(104-digit number)
33535177795193214404…56279367435006279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.707 Γ— 10¹⁰³(104-digit number)
67070355590386428809…12558734870012559361
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 289591

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 39b810f5d1ff12d9f568938b99f268533e8ced8cd40e16b070303336be43fcce

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 #289,591 on Chainz β†—
Circulating Supply:57,615,848 XPMΒ·at block #6,796,480 Β· updates every 60s
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