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Block #2,446,032

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/28/2017, 1:22:29 PM Β· Difficulty 10.9415 Β· 4,396,794 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
726b62dae83c94585fd8e808674751f68bba22d6042cc2fca53d6169d5fc8ecb
View on Chainz β†—

Height

#2,446,032

Difficulty

10.941471

Transactions

1

Size

200 B

Version

2

Bits

0af1043b

Nonce

904,804,103

Timestamp

12/28/2017, 1:22:29 PM

Confirmations

4,396,794

Mined by

⛏️ P2SHAWLr9znHhC7aWSTJqngCp9E2Gg9yZ6aZsC

Merkle Root

449feb98ec1d8fd54c1789d4ecfdec3b7218e7dc92d033def55796fac7dabe6b
Transactions (1)
Coinbase449feb98ec1d8f…5796fac7dabe6b
1 in β†’ 1 out8.3400 XPM110 B
AWLr9znH…9yZ6aZsC
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.

7.324 Γ— 10⁹⁡(96-digit number)
73241904932038456765…75672767181580701119
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
7.324 Γ— 10⁹⁡(96-digit number)
73241904932038456765…75672767181580701119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.464 Γ— 10⁹⁢(97-digit number)
14648380986407691353…51345534363161402239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.929 Γ— 10⁹⁢(97-digit number)
29296761972815382706…02691068726322804479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.859 Γ— 10⁹⁢(97-digit number)
58593523945630765412…05382137452645608959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.171 Γ— 10⁹⁷(98-digit number)
11718704789126153082…10764274905291217919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.343 Γ— 10⁹⁷(98-digit number)
23437409578252306164…21528549810582435839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.687 Γ— 10⁹⁷(98-digit number)
46874819156504612329…43057099621164871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.374 Γ— 10⁹⁷(98-digit number)
93749638313009224659…86114199242329743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.874 Γ— 10⁹⁸(99-digit number)
18749927662601844931…72228398484659486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.749 Γ— 10⁹⁸(99-digit number)
37499855325203689863…44456796969318973439
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:57,986,951 XPMΒ·at block #6,842,825 Β· updates every 60s
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