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Block #26,511

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 5:38:12 AM Β· Difficulty 7.9755 Β· 6,783,018 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ead463a2e98cd1de0d0906b12fb2aeacf5f461d55bb028992397ad6e619ebf06
View on Chainz β†—

Height

#26,511

Difficulty

7.975456

Transactions

1

Size

202 B

Version

2

Bits

07f9b77e

Nonce

1,063

Timestamp

7/13/2013, 5:38:12 AM

Confirmations

6,783,018

Mined by

⛏️ P2SHAdbcrryFEPQiAMCbjrwrmjCSyQ2cewtdYJ

Merkle Root

6d9430b11c0245dad2a171128cd6f724340ad2e8e761eebd07bd202dea930a0e
Transactions (1)
Coinbase6d9430b11c0245…bd202dea930a0e
1 in β†’ 1 out15.7000 XPM108 B
AdbcrryF…2cewtdYJ
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.

5.124 Γ— 10¹⁰³(104-digit number)
51248529608361598731…38354569283984337459
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
5.124 Γ— 10¹⁰³(104-digit number)
51248529608361598731…38354569283984337459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.024 Γ— 10¹⁰⁴(105-digit number)
10249705921672319746…76709138567968674919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.049 Γ— 10¹⁰⁴(105-digit number)
20499411843344639492…53418277135937349839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.099 Γ— 10¹⁰⁴(105-digit number)
40998823686689278984…06836554271874699679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.199 Γ— 10¹⁰⁴(105-digit number)
81997647373378557969…13673108543749399359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.639 Γ— 10¹⁰⁡(106-digit number)
16399529474675711593…27346217087498798719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.279 Γ— 10¹⁰⁡(106-digit number)
32799058949351423187…54692434174997597439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.559 Γ— 10¹⁰⁡(106-digit number)
65598117898702846375…09384868349995194879
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:57,720,310 XPMΒ·at block #6,809,528 Β· updates every 60s
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