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Block #116,796

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/14/2013, 3:27:53 PM Β· Difficulty 9.7501 Β· 6,699,958 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
830c87dc637575ffdbc5be87c692c231fa21d57f8ee809548c69d1c8c9295ff7
View on Chainz β†—

Height

#116,796

Difficulty

9.750132

Transactions

1

Size

198 B

Version

2

Bits

09c008a3

Nonce

154,149

Timestamp

8/14/2013, 3:27:53 PM

Confirmations

6,699,958

Merkle Root

f5a66b12eee3c63242032cafb2bf32bf44f4363173c30e173a1e8140a5c5e7c1
Transactions (1)
Coinbasef5a66b12eee3c6…1e8140a5c5e7c1
1 in β†’ 1 out10.5000 XPM109 B
AKErQXMS…JWgaCTzm
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.

1.992 Γ— 10⁹³(94-digit number)
19928267388426171783…55494466828349712800
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
1.992 Γ— 10⁹³(94-digit number)
19928267388426171783…55494466828349712799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.985 Γ— 10⁹³(94-digit number)
39856534776852343566…10988933656699425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.971 Γ— 10⁹³(94-digit number)
79713069553704687132…21977867313398851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.594 Γ— 10⁹⁴(95-digit number)
15942613910740937426…43955734626797702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.188 Γ— 10⁹⁴(95-digit number)
31885227821481874852…87911469253595404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.377 Γ— 10⁹⁴(95-digit number)
63770455642963749705…75822938507190809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.275 Γ— 10⁹⁡(96-digit number)
12754091128592749941…51645877014381619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.550 Γ— 10⁹⁡(96-digit number)
25508182257185499882…03291754028763238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.101 Γ— 10⁹⁡(96-digit number)
51016364514370999764…06583508057526476799
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 116796

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 830c87dc637575ffdbc5be87c692c231fa21d57f8ee809548c69d1c8c9295ff7

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 #116,796 on Chainz β†—
Circulating Supply:57,778,062 XPMΒ·at block #6,816,753 Β· updates every 60s
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