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Block #166,783

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/16/2013, 3:33:27 AM Β· Difficulty 9.8688 Β· 6,659,532 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7477bf7bf953897c53858bb4dccc30db441eb41947904cb55a845871460715e0
View on Chainz β†—

Height

#166,783

Difficulty

9.868804

Transactions

1

Size

199 B

Version

2

Bits

09de69e8

Nonce

330,557

Timestamp

9/16/2013, 3:33:27 AM

Confirmations

6,659,532

Merkle Root

b37fe03071376517fed113e57ffe1ce6a429b98c6c3f212549b16f1561624891
Transactions (1)
Coinbaseb37fe030713765…b16f1561624891
1 in β†’ 1 out10.2500 XPM109 B
Ae12LLhD…sJmChYMR
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.

4.778 Γ— 10⁹³(94-digit number)
47789605422860728620…79916770186530887780
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
4.778 Γ— 10⁹³(94-digit number)
47789605422860728620…79916770186530887781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.557 Γ— 10⁹³(94-digit number)
95579210845721457241…59833540373061775561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.911 Γ— 10⁹⁴(95-digit number)
19115842169144291448…19667080746123551121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.823 Γ— 10⁹⁴(95-digit number)
38231684338288582896…39334161492247102241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.646 Γ— 10⁹⁴(95-digit number)
76463368676577165793…78668322984494204481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.529 Γ— 10⁹⁡(96-digit number)
15292673735315433158…57336645968988408961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.058 Γ— 10⁹⁡(96-digit number)
30585347470630866317…14673291937976817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.117 Γ— 10⁹⁡(96-digit number)
61170694941261732634…29346583875953635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.223 Γ— 10⁹⁢(97-digit number)
12234138988252346526…58693167751907271681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 166783

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 7477bf7bf953897c53858bb4dccc30db441eb41947904cb55a845871460715e0

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 #166,783 on Chainz β†—
Circulating Supply:57,854,658 XPMΒ·at block #6,826,314 Β· updates every 60s
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