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Block #25,594

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 2:37:43 AM Β· Difficulty 7.9716 Β· 6,801,500 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
425ffdaf6c447493679217e2be2b4fad0450913344bf74b26f681d3b5486a5ec
View on Chainz β†—

Height

#25,594

Difficulty

7.971565

Transactions

1

Size

198 B

Version

2

Bits

07f8b87a

Nonce

480

Timestamp

7/13/2013, 2:37:43 AM

Confirmations

6,801,500

Mined by

⛏️ P2SHAJ36mt9dPGDysh1hpkWKCYpMZGNd81XoN3

Merkle Root

87e5f9a6378638652d410dbf2f50d388740f2b8b2f8e92c56f1b39aeafa95373
Transactions (1)
Coinbase87e5f9a6378638…1b39aeafa95373
1 in β†’ 1 out15.7200 XPM108 B
AJ36mt9d…Nd81XoN3
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.

9.543 Γ— 10⁹³(94-digit number)
95439826487738619383…57820685211400598639
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
9.543 Γ— 10⁹³(94-digit number)
95439826487738619383…57820685211400598639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁴(95-digit number)
19087965297547723876…15641370422801197279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.817 Γ— 10⁹⁴(95-digit number)
38175930595095447753…31282740845602394559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.635 Γ— 10⁹⁴(95-digit number)
76351861190190895506…62565481691204789119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.527 Γ— 10⁹⁡(96-digit number)
15270372238038179101…25130963382409578239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.054 Γ— 10⁹⁡(96-digit number)
30540744476076358202…50261926764819156479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.108 Γ— 10⁹⁡(96-digit number)
61081488952152716405…00523853529638312959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,860,937 XPMΒ·at block #6,827,093 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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