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Block #1,766,948

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2016, 10:02:45 AM Β· Difficulty 10.7431 Β· 5,040,260 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c07bf5e0bc21bbe3f2b44f0f29f2f034bb4b9facda4e062b47ef805f28084da
View on Chainz β†—

Height

#1,766,948

Difficulty

10.743114

Transactions

2

Size

36.83 KB

Version

2

Bits

0abe3cb8

Nonce

382,666,646

Timestamp

9/17/2016, 10:02:45 AM

Confirmations

5,040,260

Mined by

⛏️ P2SHAQag6F9HiktdFJP67aNZMH8pRiaUkZ1f3w

Merkle Root

4025200315322b43e8c029155349fd096b5e4fb5740a7df56bfe4805202f5f67
Transactions (2)
Coinbasea2caa51b55354d…e3afc3cb2376d3
1 in β†’ 1 out9.0300 XPM109 B
AQag6F9H…aUkZ1f3w
7964f43c2210b8…04bfcf6922affc
253 in β†’ 2 out20000.0100 XPM36.64 KB
AYKArr5V…V9VqiqCZAKucw7Eg…V1RnrMYJ
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.

2.309 Γ— 10⁹⁴(95-digit number)
23092215087727019467…33974000660704806719
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
2.309 Γ— 10⁹⁴(95-digit number)
23092215087727019467…33974000660704806719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.618 Γ— 10⁹⁴(95-digit number)
46184430175454038934…67948001321409613439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.236 Γ— 10⁹⁴(95-digit number)
92368860350908077868…35896002642819226879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.847 Γ— 10⁹⁡(96-digit number)
18473772070181615573…71792005285638453759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.694 Γ— 10⁹⁡(96-digit number)
36947544140363231147…43584010571276907519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.389 Γ— 10⁹⁡(96-digit number)
73895088280726462294…87168021142553815039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.477 Γ— 10⁹⁢(97-digit number)
14779017656145292458…74336042285107630079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.955 Γ— 10⁹⁢(97-digit number)
29558035312290584917…48672084570215260159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.911 Γ— 10⁹⁢(97-digit number)
59116070624581169835…97344169140430520319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.182 Γ— 10⁹⁷(98-digit number)
11823214124916233967…94688338280861040639
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:57,701,679 XPMΒ·at block #6,807,207 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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