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Block #325,819

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/23/2013, 8:34:14 AM Β· Difficulty 10.1947 Β· 6,516,908 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
918f4fa7d19551ee158ecb50212880ed114defa4f8b306b339fbcaa80b4dfca2
View on Chainz β†—

Height

#325,819

Difficulty

10.194674

Transactions

1

Size

207 B

Version

2

Bits

0a31d623

Nonce

40,848

Timestamp

12/23/2013, 8:34:14 AM

Confirmations

6,516,908

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ddd912d4684165663c057378e80e556856c4fafddf2c00755e06988008a9a84a
Transactions (1)
Coinbaseddd912d4684165…06988008a9a84a
1 in β†’ 1 out9.6100 XPM116 B
AbwWkWZt…kawDhufa
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.

7.688 Γ— 10⁹⁷(98-digit number)
76882441027239049192…34194172171288594199
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
7.688 Γ— 10⁹⁷(98-digit number)
76882441027239049192…34194172171288594199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.537 Γ— 10⁹⁸(99-digit number)
15376488205447809838…68388344342577188399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.075 Γ— 10⁹⁸(99-digit number)
30752976410895619677…36776688685154376799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.150 Γ— 10⁹⁸(99-digit number)
61505952821791239354…73553377370308753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.230 Γ— 10⁹⁹(100-digit number)
12301190564358247870…47106754740617507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.460 Γ— 10⁹⁹(100-digit number)
24602381128716495741…94213509481235014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.920 Γ— 10⁹⁹(100-digit number)
49204762257432991483…88427018962470028799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.840 Γ— 10⁹⁹(100-digit number)
98409524514865982966…76854037924940057599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.968 Γ— 10¹⁰⁰(101-digit number)
19681904902973196593…53708075849880115199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.936 Γ— 10¹⁰⁰(101-digit number)
39363809805946393186…07416151699760230399
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:57,986,155 XPMΒ·at block #6,842,726 Β· updates every 60s
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