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Home/Chain Registry/Block #171,768

Block #171,768

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2013, 6:00:13 PM Β· Difficulty 9.8637 Β· 6,654,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b09747361c8e01f09f14268e7b977018b4f185cb3dc06f0a273aa468b846f458
View on Chainz β†—

Height

#171,768

Difficulty

9.863740

Transactions

1

Size

198 B

Version

2

Bits

09dd1e11

Nonce

103,813

Timestamp

9/19/2013, 6:00:13 PM

Confirmations

6,654,965

Merkle Root

f8bf03d72b6937be6ba9299109acd30d92e6d39387722bc3a1437ac88074c161
Transactions (1)
Coinbasef8bf03d72b6937…437ac88074c161
1 in β†’ 1 out10.2600 XPM109 B
AWPh3V4b…SbWA19so
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.

5.460 Γ— 10⁹¹(92-digit number)
54602573355219733282…27016606803141347280
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
5.460 Γ— 10⁹¹(92-digit number)
54602573355219733282…27016606803141347281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.092 Γ— 10⁹²(93-digit number)
10920514671043946656…54033213606282694561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.184 Γ— 10⁹²(93-digit number)
21841029342087893312…08066427212565389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.368 Γ— 10⁹²(93-digit number)
43682058684175786625…16132854425130778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.736 Γ— 10⁹²(93-digit number)
87364117368351573251…32265708850261556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.747 Γ— 10⁹³(94-digit number)
17472823473670314650…64531417700523112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.494 Γ— 10⁹³(94-digit number)
34945646947340629300…29062835401046225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.989 Γ— 10⁹³(94-digit number)
69891293894681258601…58125670802092451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.397 Γ— 10⁹⁴(95-digit number)
13978258778936251720…16251341604184903681
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 171768

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 b09747361c8e01f09f14268e7b977018b4f185cb3dc06f0a273aa468b846f458

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 #171,768 on Chainz β†—
Circulating Supply:57,858,018 XPMΒ·at block #6,826,732 Β· updates every 60s
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