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Home/Chain Registry/Block #164,766

Block #164,766

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 9:02:08 PM Β· Difficulty 9.8637 Β· 6,652,584 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab8bc5a6ac8d79440d9397a44a6d020cdf2a00baa3a5e23b62fce6ebf7e2f6d7
View on Chainz β†—

Height

#164,766

Difficulty

9.863742

Transactions

1

Size

198 B

Version

2

Bits

09dd1e2d

Nonce

34,956

Timestamp

9/14/2013, 9:02:08 PM

Confirmations

6,652,584

Merkle Root

f7c60b8656c0eb3381f20a2ec072c295ae22978fd1a3ec5abc1c4f58820021a8
Transactions (1)
Coinbasef7c60b8656c0eb…1c4f58820021a8
1 in β†’ 1 out10.2600 XPM109 B
AJNnxqXc…Hj9ayqaW
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.

3.218 Γ— 10⁹²(93-digit number)
32187833844826517799…54222451687704258680
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.218 Γ— 10⁹²(93-digit number)
32187833844826517799…54222451687704258679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.437 Γ— 10⁹²(93-digit number)
64375667689653035598…08444903375408517359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.287 Γ— 10⁹³(94-digit number)
12875133537930607119…16889806750817034719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.575 Γ— 10⁹³(94-digit number)
25750267075861214239…33779613501634069439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.150 Γ— 10⁹³(94-digit number)
51500534151722428479…67559227003268138879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁴(95-digit number)
10300106830344485695…35118454006536277759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.060 Γ— 10⁹⁴(95-digit number)
20600213660688971391…70236908013072555519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.120 Γ— 10⁹⁴(95-digit number)
41200427321377942783…40473816026145111039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.240 Γ— 10⁹⁴(95-digit number)
82400854642755885566…80947632052290222079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.648 Γ— 10⁹⁡(96-digit number)
16480170928551177113…61895264104580444159
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 164766

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 ab8bc5a6ac8d79440d9397a44a6d020cdf2a00baa3a5e23b62fce6ebf7e2f6d7

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 #164,766 on Chainz β†—
Circulating Supply:57,782,847 XPMΒ·at block #6,817,349 Β· updates every 60s
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