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Block #1,452,017

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/11/2016, 4:02:28 PM Β· Difficulty 10.7364 Β· 5,390,101 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
970e5a19ae62ffd3fe9f60e13e24f678df94ac2dc9839c6beab7f9192e5e90f5
View on Chainz β†—

Height

#1,452,017

Difficulty

10.736361

Transactions

1

Size

199 B

Version

2

Bits

0abc8224

Nonce

1,181,393,437

Timestamp

2/11/2016, 4:02:28 PM

Confirmations

5,390,101

Mined by

⛏️ P2SHAVd77bTJkDcKY9wFkNwA5ExjwjNVo1rWzD

Merkle Root

cedf6c4446ea5429f00d59d2a0cd6c5f0d2171d0bd0456fe0b14fdefd914b374
Transactions (1)
Coinbasecedf6c4446ea54…14fdefd914b374
1 in β†’ 1 out8.6600 XPM109 B
AVd77bTJ…NVo1rWzD
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.

4.400 Γ— 10⁹⁴(95-digit number)
44009480165905067188…86101579969076346239
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
4.400 Γ— 10⁹⁴(95-digit number)
44009480165905067188…86101579969076346239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.801 Γ— 10⁹⁴(95-digit number)
88018960331810134376…72203159938152692479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.760 Γ— 10⁹⁡(96-digit number)
17603792066362026875…44406319876305384959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.520 Γ— 10⁹⁡(96-digit number)
35207584132724053750…88812639752610769919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.041 Γ— 10⁹⁡(96-digit number)
70415168265448107501…77625279505221539839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.408 Γ— 10⁹⁢(97-digit number)
14083033653089621500…55250559010443079679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.816 Γ— 10⁹⁢(97-digit number)
28166067306179243000…10501118020886159359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.633 Γ— 10⁹⁢(97-digit number)
56332134612358486000…21002236041772318719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.126 Γ— 10⁹⁷(98-digit number)
11266426922471697200…42004472083544637439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.253 Γ— 10⁹⁷(98-digit number)
22532853844943394400…84008944167089274879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.506 Γ— 10⁹⁷(98-digit number)
45065707689886788800…68017888334178549759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,981,331 XPMΒ·at block #6,842,117 Β· updates every 60s
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