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Home/Chain Registry/Block #164,829

Block #164,829

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 9:59:35 PM Β· Difficulty 9.8639 Β· 6,631,021 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
80e21f4efb684fe5a958dd1a225c79a6b074fc99d15a28f8bcb93af6c5a2b3cf
View on Chainz β†—

Height

#164,829

Difficulty

9.863896

Transactions

1

Size

200 B

Version

2

Bits

09dd2848

Nonce

16,780,256

Timestamp

9/14/2013, 9:59:35 PM

Confirmations

6,631,021

Merkle Root

48f80a33f6e6715fc1f56479c0f44f460f087d4fd25c0f8915724470ad7350de
Transactions (1)
Coinbase48f80a33f6e671…724470ad7350de
1 in β†’ 1 out10.2600 XPM112 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.

8.620 Γ— 10⁸⁹(90-digit number)
86209429414951257544…12791879660996224240
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
8.620 Γ— 10⁸⁹(90-digit number)
86209429414951257544…12791879660996224239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.724 Γ— 10⁹⁰(91-digit number)
17241885882990251508…25583759321992448479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.448 Γ— 10⁹⁰(91-digit number)
34483771765980503017…51167518643984896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.896 Γ— 10⁹⁰(91-digit number)
68967543531961006035…02335037287969793919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.379 Γ— 10⁹¹(92-digit number)
13793508706392201207…04670074575939587839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.758 Γ— 10⁹¹(92-digit number)
27587017412784402414…09340149151879175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.517 Γ— 10⁹¹(92-digit number)
55174034825568804828…18680298303758351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.103 Γ— 10⁹²(93-digit number)
11034806965113760965…37360596607516702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.206 Γ— 10⁹²(93-digit number)
22069613930227521931…74721193215033405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.413 Γ— 10⁹²(93-digit number)
44139227860455043862…49442386430066810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.827 Γ— 10⁹²(93-digit number)
88278455720910087725…98884772860133621759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 164829

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 80e21f4efb684fe5a958dd1a225c79a6b074fc99d15a28f8bcb93af6c5a2b3cf

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 #164,829 on Chainz β†—
Circulating Supply:57,610,885 XPMΒ·at block #6,795,849 Β· updates every 60s
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