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Block #25,595

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 2:37:46 AM Β· Difficulty 7.9716 Β· 6,800,677 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4cb93c0072c97ae7bf10b1f8a1f0a68ea03f3126153cd9aae00054ab113e5335
View on Chainz β†—

Height

#25,595

Difficulty

7.971569

Transactions

2

Size

357 B

Version

2

Bits

07f8b8c1

Nonce

3

Timestamp

7/13/2013, 2:37:46 AM

Confirmations

6,800,677

Merkle Root

f2f338c7076e81aaa1579518f26351d8e379d9a229d1230a16e14083ddc20eb2
Transactions (2)
Coinbasea958543b4045fb…c87189e24916b9
1 in β†’ 1 out15.7300 XPM109 B
AQmvEDXt…1BYA7VRt
e0b24ab6e122df…24fd9ed1852856
1 in β†’ 1 out15.7900 XPM159 B
AMUE7KWu…CqH5CJVk
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.

2.386 Γ— 10⁹²(93-digit number)
23866690730332099688…78136732732882493540
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
2.386 Γ— 10⁹²(93-digit number)
23866690730332099688…78136732732882493539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.773 Γ— 10⁹²(93-digit number)
47733381460664199376…56273465465764987079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.546 Γ— 10⁹²(93-digit number)
95466762921328398752…12546930931529974159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.909 Γ— 10⁹³(94-digit number)
19093352584265679750…25093861863059948319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.818 Γ— 10⁹³(94-digit number)
38186705168531359500…50187723726119896639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.637 Γ— 10⁹³(94-digit number)
76373410337062719001…00375447452239793279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.527 Γ— 10⁹⁴(95-digit number)
15274682067412543800…00750894904479586559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.054 Γ— 10⁹⁴(95-digit number)
30549364134825087600…01501789808959173119
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 25595

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 4cb93c0072c97ae7bf10b1f8a1f0a68ea03f3126153cd9aae00054ab113e5335

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 #25,595 on Chainz β†—
Circulating Supply:57,854,312 XPMΒ·at block #6,826,271 Β· updates every 60s
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