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Block #82,261

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2013, 7:19:07 AM Β· Difficulty 9.2761 Β· 6,727,259 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3cf138d08a6bfeab05cde8f5f986e022e93028b6c03316ee3e60980a8d4a03b0
View on Chainz β†—

Height

#82,261

Difficulty

9.276101

Transactions

2

Size

1.41 KB

Version

2

Bits

0946ae91

Nonce

6,710

Timestamp

7/25/2013, 7:19:07 AM

Confirmations

6,727,259

Mined by

⛏️ P2SHAM1oxmyDNoy3zuFVAiagFA4yGKGu3w2GXt

Merkle Root

68b93639939d24121b0671c87528d0e951850fec54bc24806ab496355e888197
Transactions (2)
Coinbased4d39b76ee9a7d…a2e580351f43c4
1 in β†’ 1 out11.6300 XPM109 B
AM1oxmyD…Gu3w2GXt
c0ee5994fd2825…29a96a012dd62f
10 in β†’ 1 out100.0000 XPM1.22 KB
AHhg9WyM…nTicvK7Y
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.

5.057 Γ— 10⁹³(94-digit number)
50577427138479945997…48932751914936597319
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
5.057 Γ— 10⁹³(94-digit number)
50577427138479945997…48932751914936597319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁴(95-digit number)
10115485427695989199…97865503829873194639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.023 Γ— 10⁹⁴(95-digit number)
20230970855391978398…95731007659746389279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.046 Γ— 10⁹⁴(95-digit number)
40461941710783956797…91462015319492778559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.092 Γ— 10⁹⁴(95-digit number)
80923883421567913595…82924030638985557119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.618 Γ— 10⁹⁡(96-digit number)
16184776684313582719…65848061277971114239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.236 Γ— 10⁹⁡(96-digit number)
32369553368627165438…31696122555942228479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.473 Γ— 10⁹⁡(96-digit number)
64739106737254330876…63392245111884456959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.294 Γ— 10⁹⁢(97-digit number)
12947821347450866175…26784490223768913919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,720,236 XPMΒ·at block #6,809,519 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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