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Home/Chain Registry/Block #1,729,173

Block #1,729,173

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/22/2016, 2:10:28 PM Β· Difficulty 10.7102 Β· 5,116,146 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c20643fbf990eb0ab748dbac9b06cc7ec0f26d462da345006dd1b4a3e10a35c4
View on Chainz β†—

Difficulty

10.710230

Transactions

1

Size

199 B

Version

2

Bits

0ab5d19e

Nonce

341,828,394

Timestamp

8/22/2016, 2:10:28 PM

Confirmations

5,116,146

Merkle Root

ce97442b1c2d72cbf91035ecbf05b205d06d9c535f06ec70b22093af91f1df6e
Transactions (1)
Coinbasece97442b1c2d72…2093af91f1df6e
1 in β†’ 1 out8.7000 XPM109 B
AKkXrjFX…oTVZwUSo
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.

3.002 Γ— 10⁹³(94-digit number)
30026107183499584182…37109428523098207820
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
3.002 Γ— 10⁹³(94-digit number)
30026107183499584182…37109428523098207819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.005 Γ— 10⁹³(94-digit number)
60052214366999168364…74218857046196415639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.201 Γ— 10⁹⁴(95-digit number)
12010442873399833672…48437714092392831279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.402 Γ— 10⁹⁴(95-digit number)
24020885746799667345…96875428184785662559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.804 Γ— 10⁹⁴(95-digit number)
48041771493599334691…93750856369571325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.608 Γ— 10⁹⁴(95-digit number)
96083542987198669382…87501712739142650239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.921 Γ— 10⁹⁡(96-digit number)
19216708597439733876…75003425478285300479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.843 Γ— 10⁹⁡(96-digit number)
38433417194879467753…50006850956570600959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.686 Γ— 10⁹⁡(96-digit number)
76866834389758935506…00013701913141201919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.537 Γ— 10⁹⁢(97-digit number)
15373366877951787101…00027403826282403839
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 1729173

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 c20643fbf990eb0ab748dbac9b06cc7ec0f26d462da345006dd1b4a3e10a35c4

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 #1,729,173 on Chainz β†—
Circulating Supply:58,006,990 XPMΒ·at block #6,845,318 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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