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Block #236,122

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/31/2013, 8:02:57 AM Β· Difficulty 9.9468 Β· 6,590,854 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
355be834bb850385b2342bad7f60807baa10169e840def4e9a54f5a5ae1f2f55
View on Chainz β†—

Height

#236,122

Difficulty

9.946755

Transactions

1

Size

207 B

Version

2

Bits

09f25e8e

Nonce

67,109,131

Timestamp

10/31/2013, 8:02:57 AM

Confirmations

6,590,854

Merkle Root

5fecb4c162b3667ac16b3f303f7e2a14fe4e050781e7787a4cec6b5b3060737d
Transactions (1)
Coinbase5fecb4c162b366…ec6b5b3060737d
1 in β†’ 1 out10.0900 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.135 Γ— 10⁹⁢(97-digit number)
51358801041193267815…69811140460530135040
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
5.135 Γ— 10⁹⁢(97-digit number)
51358801041193267815…69811140460530135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.027 Γ— 10⁹⁷(98-digit number)
10271760208238653563…39622280921060270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.054 Γ— 10⁹⁷(98-digit number)
20543520416477307126…79244561842120540159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.108 Γ— 10⁹⁷(98-digit number)
41087040832954614252…58489123684241080319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.217 Γ— 10⁹⁷(98-digit number)
82174081665909228505…16978247368482160639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.643 Γ— 10⁹⁸(99-digit number)
16434816333181845701…33956494736964321279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.286 Γ— 10⁹⁸(99-digit number)
32869632666363691402…67912989473928642559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.573 Γ— 10⁹⁸(99-digit number)
65739265332727382804…35825978947857285119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.314 Γ— 10⁹⁹(100-digit number)
13147853066545476560…71651957895714570239
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 236122

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 355be834bb850385b2342bad7f60807baa10169e840def4e9a54f5a5ae1f2f55

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 #236,122 on Chainz β†—
Circulating Supply:57,859,983 XPMΒ·at block #6,826,975 Β· updates every 60s
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