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Block #1,850,552

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/15/2016, 7:31:18 PM Β· Difficulty 10.6289 Β· 4,986,136 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2836f5314ef1c77d6cb55a31d87b197884cf54175cfaf35a9d3bfc7041e883eb
View on Chainz β†—

Height

#1,850,552

Difficulty

10.628943

Transactions

1

Size

242 B

Version

2

Bits

0aa10265

Nonce

514,973,201

Timestamp

11/15/2016, 7:31:18 PM

Confirmations

4,986,136

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

a7e71a3d963e7a49ec7ea7c87161e4d580e1bc61e4db21dd6853b3e69c95c20d
Transactions (1)
Coinbasea7e71a3d963e7a…53b3e69c95c20d
1 in β†’ 2 out8.8400 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

3.082 Γ— 10⁹⁡(96-digit number)
30825938441769009935…19836015145153941759
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
3.082 Γ— 10⁹⁡(96-digit number)
30825938441769009935…19836015145153941759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.165 Γ— 10⁹⁡(96-digit number)
61651876883538019870…39672030290307883519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.233 Γ— 10⁹⁢(97-digit number)
12330375376707603974…79344060580615767039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.466 Γ— 10⁹⁢(97-digit number)
24660750753415207948…58688121161231534079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.932 Γ— 10⁹⁢(97-digit number)
49321501506830415896…17376242322463068159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.864 Γ— 10⁹⁢(97-digit number)
98643003013660831792…34752484644926136319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.972 Γ— 10⁹⁷(98-digit number)
19728600602732166358…69504969289852272639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.945 Γ— 10⁹⁷(98-digit number)
39457201205464332717…39009938579704545279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.891 Γ— 10⁹⁷(98-digit number)
78914402410928665434…78019877159409090559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.578 Γ— 10⁹⁸(99-digit number)
15782880482185733086…56039754318818181119
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:57,937,786 XPMΒ·at block #6,836,687 Β· updates every 60s
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