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Block #173,381

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/20/2013, 10:42:08 PM Β· Difficulty 9.8609 Β· 6,653,752 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4219807e37372692e67beb50b5a7fc8c64f13a58a67ad560d46c5e2559b30549
View on Chainz β†—

Height

#173,381

Difficulty

9.860878

Transactions

1

Size

198 B

Version

2

Bits

09dc6283

Nonce

33,777

Timestamp

9/20/2013, 10:42:08 PM

Confirmations

6,653,752

Merkle Root

2c75f65183dd5c90e000ea510585ab3b72b151bfe719db1c828b43266ce99728
Transactions (1)
Coinbase2c75f65183dd5c…8b43266ce99728
1 in β†’ 1 out10.2700 XPM109 B
AXX6Uqo6…r1CYovnd
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.

2.008 Γ— 10⁹²(93-digit number)
20081687708427026340…64698552956304846880
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
2.008 Γ— 10⁹²(93-digit number)
20081687708427026340…64698552956304846879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.016 Γ— 10⁹²(93-digit number)
40163375416854052681…29397105912609693759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.032 Γ— 10⁹²(93-digit number)
80326750833708105363…58794211825219387519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.606 Γ— 10⁹³(94-digit number)
16065350166741621072…17588423650438775039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.213 Γ— 10⁹³(94-digit number)
32130700333483242145…35176847300877550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.426 Γ— 10⁹³(94-digit number)
64261400666966484291…70353694601755100159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁴(95-digit number)
12852280133393296858…40707389203510200319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.570 Γ— 10⁹⁴(95-digit number)
25704560266786593716…81414778407020400639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.140 Γ— 10⁹⁴(95-digit number)
51409120533573187432…62829556814040801279
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 173381

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 4219807e37372692e67beb50b5a7fc8c64f13a58a67ad560d46c5e2559b30549

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 #173,381 on Chainz β†—
Circulating Supply:57,861,244 XPMΒ·at block #6,827,132 Β· updates every 60s
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