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Block #1,808,307

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2016, 5:15:21 PM Β· Difficulty 10.8300 Β· 5,031,069 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
11e5e2fe44b6bf014fe0ba5e8a8267da1650f51adbe4ec7c1bee8b2c9daa1c3d
View on Chainz β†—

Height

#1,808,307

Difficulty

10.829997

Transactions

2

Size

2.87 KB

Version

2

Bits

0ad47ab7

Nonce

1,823,857,004

Timestamp

10/14/2016, 5:15:21 PM

Confirmations

5,031,069

Mined by

⛏️ P2SHAYo1GJHPrDDmjLUQb6cenrtXAue3vHEzi8

Merkle Root

9efc45abacd43ae619a5a6e7994069389bb53f07392dfa3d3e3f3e47cfd1ae5c
Transactions (2)
Coinbase7f247b61262f83…1cc7e0f508fd0c
1 in β†’ 1 out8.6100 XPM110 B
AYo1GJHP…e3vHEzi8
3b037f1825bcc8…340be9e8eb7daf
18 in β†’ 2 out59.1573 XPM2.68 KB
AGthQtqE…21VZ3RyVAGjfN59n…XRyWCGwx
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.

2.360 Γ— 10⁹⁡(96-digit number)
23602828140188377207…48314392910301865439
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
2.360 Γ— 10⁹⁡(96-digit number)
23602828140188377207…48314392910301865439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.720 Γ— 10⁹⁡(96-digit number)
47205656280376754414…96628785820603730879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.441 Γ— 10⁹⁡(96-digit number)
94411312560753508828…93257571641207461759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.888 Γ— 10⁹⁢(97-digit number)
18882262512150701765…86515143282414923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.776 Γ— 10⁹⁢(97-digit number)
37764525024301403531…73030286564829847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.552 Γ— 10⁹⁢(97-digit number)
75529050048602807062…46060573129659694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.510 Γ— 10⁹⁷(98-digit number)
15105810009720561412…92121146259319388159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.021 Γ— 10⁹⁷(98-digit number)
30211620019441122825…84242292518638776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.042 Γ— 10⁹⁷(98-digit number)
60423240038882245650…68484585037277552639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.208 Γ— 10⁹⁸(99-digit number)
12084648007776449130…36969170074555105279
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:57,959,291 XPMΒ·at block #6,839,375 Β· updates every 60s
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