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Block #171,356

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/19/2013, 10:43:22 AM Β· Difficulty 9.8644 Β· 6,635,270 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee7a2efcfb0ae8e7abb78f10440302cc69e8c8a3176ee062884e63bd22f4a9c8
View on Chainz β†—

Height

#171,356

Difficulty

9.864380

Transactions

1

Size

198 B

Version

2

Bits

09dd47fa

Nonce

135,295

Timestamp

9/19/2013, 10:43:22 AM

Confirmations

6,635,270

Merkle Root

e7231059121cbe1f21177d9916d350ee16c3faa6408bfc39df53ea2257acbc19
Transactions (1)
Coinbasee7231059121cbe…53ea2257acbc19
1 in β†’ 1 out10.2600 XPM109 B
AFus8LE3…8d9qs8De
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.

1.831 Γ— 10⁹²(93-digit number)
18317770032745643819…20798192156143517320
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
1.831 Γ— 10⁹²(93-digit number)
18317770032745643819…20798192156143517319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.663 Γ— 10⁹²(93-digit number)
36635540065491287638…41596384312287034639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.327 Γ— 10⁹²(93-digit number)
73271080130982575277…83192768624574069279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.465 Γ— 10⁹³(94-digit number)
14654216026196515055…66385537249148138559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.930 Γ— 10⁹³(94-digit number)
29308432052393030111…32771074498296277119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.861 Γ— 10⁹³(94-digit number)
58616864104786060222…65542148996592554239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.172 Γ— 10⁹⁴(95-digit number)
11723372820957212044…31084297993185108479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.344 Γ— 10⁹⁴(95-digit number)
23446745641914424088…62168595986370216959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.689 Γ— 10⁹⁴(95-digit number)
46893491283828848177…24337191972740433919
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 171356

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 ee7a2efcfb0ae8e7abb78f10440302cc69e8c8a3176ee062884e63bd22f4a9c8

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 #171,356 on Chainz β†—
Circulating Supply:57,697,107 XPMΒ·at block #6,806,625 Β· updates every 60s
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