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Block #851,635

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2014, 11:17:06 AM Β· Difficulty 10.9704 Β· 5,990,674 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5fb7391a65150d5e8a5d7a6bac9dcdc29a5412ee821c48159d6fbbfb53ae7e35
View on Chainz β†—

Height

#851,635

Difficulty

10.970410

Transactions

1

Size

206 B

Version

2

Bits

0af86cd0

Nonce

552,691,823

Timestamp

12/13/2014, 11:17:06 AM

Confirmations

5,990,674

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e216c3557fbde971a1c539fc8dd90d4259e3301cf09377a7f64971098ad768f7
Transactions (1)
Coinbasee216c3557fbde9…4971098ad768f7
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

8.699 Γ— 10⁹³(94-digit number)
86993864296309713695…62725760717985520639
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
8.699 Γ— 10⁹³(94-digit number)
86993864296309713695…62725760717985520639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.739 Γ— 10⁹⁴(95-digit number)
17398772859261942739…25451521435971041279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.479 Γ— 10⁹⁴(95-digit number)
34797545718523885478…50903042871942082559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.959 Γ— 10⁹⁴(95-digit number)
69595091437047770956…01806085743884165119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.391 Γ— 10⁹⁡(96-digit number)
13919018287409554191…03612171487768330239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.783 Γ— 10⁹⁡(96-digit number)
27838036574819108382…07224342975536660479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.567 Γ— 10⁹⁡(96-digit number)
55676073149638216764…14448685951073320959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁢(97-digit number)
11135214629927643352…28897371902146641919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁢(97-digit number)
22270429259855286705…57794743804293283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.454 Γ— 10⁹⁢(97-digit number)
44540858519710573411…15589487608586567679
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:57,982,878 XPMΒ·at block #6,842,308 Β· updates every 60s
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