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Home/Chain Registry/Block #172,731

Block #172,731

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/20/2013, 11:28:53 AM Β· Difficulty 9.8615 Β· 6,644,397 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
482e4a6cd19c8f48a3594d04e2b6ec88c5bd0ab2b85ebda315b7a012fa7d9300
View on Chainz β†—

Height

#172,731

Difficulty

9.861498

Transactions

1

Size

200 B

Version

2

Bits

09dc8b1c

Nonce

32,876

Timestamp

9/20/2013, 11:28:53 AM

Confirmations

6,644,397

Merkle Root

76d93be0389bcf7dd7dd2bbb86bc22f76961f797445f19b7e9aed4c779b6210d
Transactions (1)
Coinbase76d93be0389bcf…aed4c779b6210d
1 in β†’ 1 out10.2700 XPM109 B
AM1A9CZL…as4Lpogj
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.

1.702 Γ— 10⁹⁷(98-digit number)
17026117992129153484…99986180510933084160
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
1.702 Γ— 10⁹⁷(98-digit number)
17026117992129153484…99986180510933084159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.405 Γ— 10⁹⁷(98-digit number)
34052235984258306969…99972361021866168319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.810 Γ— 10⁹⁷(98-digit number)
68104471968516613938…99944722043732336639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.362 Γ— 10⁹⁸(99-digit number)
13620894393703322787…99889444087464673279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.724 Γ— 10⁹⁸(99-digit number)
27241788787406645575…99778888174929346559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.448 Γ— 10⁹⁸(99-digit number)
54483577574813291150…99557776349858693119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.089 Γ— 10⁹⁹(100-digit number)
10896715514962658230…99115552699717386239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.179 Γ— 10⁹⁹(100-digit number)
21793431029925316460…98231105399434772479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.358 Γ— 10⁹⁹(100-digit number)
43586862059850632920…96462210798869544959
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 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
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 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 172731

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 482e4a6cd19c8f48a3594d04e2b6ec88c5bd0ab2b85ebda315b7a012fa7d9300

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 #172,731 on Chainz β†—
Circulating Supply:57,781,058 XPMΒ·at block #6,817,127 Β· updates every 60s
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