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Block #242,202

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2013, 3:17:53 PM Β· Difficulty 9.9593 Β· 6,588,711 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa88fd0578e3c21e981265ce9f95154a275e12f2e2c99ee6e64a773876692946
View on Chainz β†—

Height

#242,202

Difficulty

9.959294

Transactions

2

Size

1.14 KB

Version

2

Bits

09f59447

Nonce

27,940

Timestamp

11/3/2013, 3:17:53 PM

Confirmations

6,588,711

Merkle Root

af42397797b1ae791730b00c4d3b911af45a4f6cd95d8afce4088bc3271b5bf6
Transactions (2)
Coinbase194d200937a834…9bef4c5f6c2819
1 in β†’ 1 out10.0900 XPM109 B
ASp65MBT…h6BHkvcu
f1aec6776190c9…fdf94c6acd9b2f
6 in β†’ 2 out1.0140 XPM965 B
AGkot61R…H6g4jUEpAdxpgmLw…1ZHpWnuT
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.

1.313 Γ— 10⁹⁴(95-digit number)
13139223976126831294…52174258443387013120
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
1.313 Γ— 10⁹⁴(95-digit number)
13139223976126831294…52174258443387013119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.627 Γ— 10⁹⁴(95-digit number)
26278447952253662589…04348516886774026239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.255 Γ— 10⁹⁴(95-digit number)
52556895904507325178…08697033773548052479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.051 Γ— 10⁹⁡(96-digit number)
10511379180901465035…17394067547096104959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.102 Γ— 10⁹⁡(96-digit number)
21022758361802930071…34788135094192209919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.204 Γ— 10⁹⁡(96-digit number)
42045516723605860143…69576270188384419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.409 Γ— 10⁹⁡(96-digit number)
84091033447211720286…39152540376768839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.681 Γ— 10⁹⁢(97-digit number)
16818206689442344057…78305080753537679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.363 Γ— 10⁹⁢(97-digit number)
33636413378884688114…56610161507075358719
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 242202

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 aa88fd0578e3c21e981265ce9f95154a275e12f2e2c99ee6e64a773876692946

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 #242,202 on Chainz β†—
Circulating Supply:57,891,433 XPMΒ·at block #6,830,912 Β· updates every 60s
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