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Block #2,087,094

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/25/2017, 10:53:11 AM Β· Difficulty 10.8740 Β· 4,754,042 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c169c8aab54b8c36db6f6436634a473fe377474dcfad66300dcbc38d5278bd77
View on Chainz β†—

Height

#2,087,094

Difficulty

10.874039

Transactions

1

Size

199 B

Version

2

Bits

0adfc104

Nonce

1,330,111,991

Timestamp

4/25/2017, 10:53:11 AM

Confirmations

4,754,042

Mined by

⛏️ P2SHATUYKPvNt1BNzcsf2uQu8RMFrLUYNUkkzz

Merkle Root

1da763ef2b81c80371fe463e9b6a4116443f269da4ba6cc6104b3392a39dd295
Transactions (1)
Coinbase1da763ef2b81c8…4b3392a39dd295
1 in β†’ 1 out8.4400 XPM109 B
ATUYKPvN…UYNUkkzz
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.

3.167 Γ— 10⁹⁡(96-digit number)
31672791830246030210…07060033700676298559
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
3.167 Γ— 10⁹⁡(96-digit number)
31672791830246030210…07060033700676298559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.334 Γ— 10⁹⁡(96-digit number)
63345583660492060421…14120067401352597119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.266 Γ— 10⁹⁢(97-digit number)
12669116732098412084…28240134802705194239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.533 Γ— 10⁹⁢(97-digit number)
25338233464196824168…56480269605410388479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.067 Γ— 10⁹⁢(97-digit number)
50676466928393648336…12960539210820776959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.013 Γ— 10⁹⁷(98-digit number)
10135293385678729667…25921078421641553919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.027 Γ— 10⁹⁷(98-digit number)
20270586771357459334…51842156843283107839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.054 Γ— 10⁹⁷(98-digit number)
40541173542714918669…03684313686566215679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.108 Γ— 10⁹⁷(98-digit number)
81082347085429837338…07368627373132431359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.621 Γ— 10⁹⁸(99-digit number)
16216469417085967467…14737254746264862719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,973,450 XPMΒ·at block #6,841,135 Β· updates every 60s
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