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Block #26,204

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 4:38:07 AM Β· Difficulty 7.9742 Β· 6,791,440 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
daf8992fa6525ec091e7f99a0241fd8a3c34fa6b8ab55c08dafa75c37a0277dc
View on Chainz β†—

Height

#26,204

Difficulty

7.974215

Transactions

1

Size

199 B

Version

2

Bits

07f96628

Nonce

155

Timestamp

7/13/2013, 4:38:07 AM

Confirmations

6,791,440

Merkle Root

12a9a9ee39d9ee4f0d85581d2605fd6dc7067bbf2afe5838c3312417aab38472
Transactions (1)
Coinbase12a9a9ee39d9ee…312417aab38472
1 in β†’ 1 out15.7100 XPM108 B
AS9VQGRx…kfZ9rttr
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.

9.621 Γ— 10⁹⁡(96-digit number)
96215470966592040052…37058057069209883420
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
9.621 Γ— 10⁹⁡(96-digit number)
96215470966592040052…37058057069209883419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.924 Γ— 10⁹⁢(97-digit number)
19243094193318408010…74116114138419766839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.848 Γ— 10⁹⁢(97-digit number)
38486188386636816020…48232228276839533679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.697 Γ— 10⁹⁢(97-digit number)
76972376773273632041…96464456553679067359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.539 Γ— 10⁹⁷(98-digit number)
15394475354654726408…92928913107358134719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.078 Γ— 10⁹⁷(98-digit number)
30788950709309452816…85857826214716269439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.157 Γ— 10⁹⁷(98-digit number)
61577901418618905633…71715652429432538879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.231 Γ— 10⁹⁸(99-digit number)
12315580283723781126…43431304858865077759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 26204

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 daf8992fa6525ec091e7f99a0241fd8a3c34fa6b8ab55c08dafa75c37a0277dc

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 #26,204 on Chainz β†—
Circulating Supply:57,785,203 XPMΒ·at block #6,817,643 Β· updates every 60s
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