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Block #115,203

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/13/2013, 3:23:30 PM Β· Difficulty 9.7426 Β· 6,710,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c19f9022624ac673160dc59ca9c9fce67712a0e227dc9c32beb89081e76bee61
View on Chainz β†—

Height

#115,203

Difficulty

9.742615

Transactions

2

Size

574 B

Version

2

Bits

09be1c00

Nonce

34,944

Timestamp

8/13/2013, 3:23:30 PM

Confirmations

6,710,481

Merkle Root

8022503745d86bb5c77babf7fe9625eff86420199684ef9df7b0c861f8ca38dd
Transactions (2)
Coinbasec9d4f9676eb993…ae847df6798e59
1 in β†’ 1 out10.5300 XPM109 B
AGXS5BR4…WtNUVc3H
53c65364884a82…6272f60a8d0739
2 in β†’ 2 out2.4799 XPM374 B
AP4exjFF…2JJqgYeiAdT8QD3t…V3EWtttA
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.

2.378 Γ— 10⁹⁷(98-digit number)
23785507334908461528…30436899965284368340
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
2.378 Γ— 10⁹⁷(98-digit number)
23785507334908461528…30436899965284368339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.757 Γ— 10⁹⁷(98-digit number)
47571014669816923056…60873799930568736679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.514 Γ— 10⁹⁷(98-digit number)
95142029339633846112…21747599861137473359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.902 Γ— 10⁹⁸(99-digit number)
19028405867926769222…43495199722274946719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.805 Γ— 10⁹⁸(99-digit number)
38056811735853538445…86990399444549893439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.611 Γ— 10⁹⁸(99-digit number)
76113623471707076890…73980798889099786879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁹(100-digit number)
15222724694341415378…47961597778199573759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.044 Γ— 10⁹⁹(100-digit number)
30445449388682830756…95923195556399147519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.089 Γ— 10⁹⁹(100-digit number)
60890898777365661512…91846391112798295039
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 115203

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 c19f9022624ac673160dc59ca9c9fce67712a0e227dc9c32beb89081e76bee61

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 #115,203 on Chainz β†—
Circulating Supply:57,849,582 XPMΒ·at block #6,825,683 Β· updates every 60s
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