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Block #25,992

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 3:55:58 AM Β· Difficulty 7.9733 Β· 6,777,337 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c781c2005738d8f85630045bab7268d8f08998acfba19fa60888039fe6c7ed0c
View on Chainz β†—

Height

#25,992

Difficulty

7.973323

Transactions

1

Size

200 B

Version

2

Bits

07f92bb4

Nonce

2,144

Timestamp

7/13/2013, 3:55:58 AM

Confirmations

6,777,337

Mined by

⛏️ P2SHAT4LjEXDr4LRvxnYpgc1TsMF9rcE6sWKJA

Merkle Root

f445d167d63b93c3ba88f8bfb600509af69ee946dd5389da89bb498c1993b390
Transactions (1)
Coinbasef445d167d63b93…bb498c1993b390
1 in β†’ 1 out15.7100 XPM108 B
AT4LjEXD…cE6sWKJA
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.

1.694 Γ— 10⁹⁸(99-digit number)
16944818416352858730…24501174633483698399
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
1.694 Γ— 10⁹⁸(99-digit number)
16944818416352858730…24501174633483698399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.388 Γ— 10⁹⁸(99-digit number)
33889636832705717460…49002349266967396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.777 Γ— 10⁹⁸(99-digit number)
67779273665411434921…98004698533934793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.355 Γ— 10⁹⁹(100-digit number)
13555854733082286984…96009397067869587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.711 Γ— 10⁹⁹(100-digit number)
27111709466164573968…92018794135739174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.422 Γ— 10⁹⁹(100-digit number)
54223418932329147936…84037588271478348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.084 Γ— 10¹⁰⁰(101-digit number)
10844683786465829587…68075176542956697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.168 Γ— 10¹⁰⁰(101-digit number)
21689367572931659174…36150353085913395199
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

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:57,670,663 XPMΒ·at block #6,803,328 Β· updates every 60s
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