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Block #1,611,752

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/3/2016, 1:54:08 AM Β· Difficulty 10.6052 Β· 5,230,634 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
757cf9f224dc76bbe1085cd8114678ef135899aa0cb443b0c1c1c1bf1d97f417
View on Chainz β†—

Height

#1,611,752

Difficulty

10.605202

Transactions

1

Size

200 B

Version

2

Bits

0a9aee8b

Nonce

1,031,509,324

Timestamp

6/3/2016, 1:54:08 AM

Confirmations

5,230,634

Mined by

⛏️ P2SHAYC8UPa3BkUrxYLcgMRGgnMbWNy8qutef7

Merkle Root

b6aad8f441361764df0ed9c659f5e49d6aa3eb46d1d6fea226e62e72153290c4
Transactions (1)
Coinbaseb6aad8f4413617…e62e72153290c4
1 in β†’ 1 out8.8800 XPM109 B
AYC8UPa3…y8qutef7
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.

9.116 Γ— 10⁹⁢(97-digit number)
91165966837118910583…78792377734126704639
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
9.116 Γ— 10⁹⁢(97-digit number)
91165966837118910583…78792377734126704639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.823 Γ— 10⁹⁷(98-digit number)
18233193367423782116…57584755468253409279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.646 Γ— 10⁹⁷(98-digit number)
36466386734847564233…15169510936506818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.293 Γ— 10⁹⁷(98-digit number)
72932773469695128466…30339021873013637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.458 Γ— 10⁹⁸(99-digit number)
14586554693939025693…60678043746027274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.917 Γ— 10⁹⁸(99-digit number)
29173109387878051386…21356087492054548479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.834 Γ— 10⁹⁸(99-digit number)
58346218775756102773…42712174984109096959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁹(100-digit number)
11669243755151220554…85424349968218193919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.333 Γ— 10⁹⁹(100-digit number)
23338487510302441109…70848699936436387839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.667 Γ— 10⁹⁹(100-digit number)
46676975020604882218…41697399872872775679
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:57,983,497 XPMΒ·at block #6,842,385 Β· updates every 60s
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