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Block #442,116

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/13/2014, 2:27:45 PM Β· Difficulty 10.3524 Β· 6,384,642 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
20b1a7a23c02d588ec4f125066ad78db7f3d295e5bf2b637f18e1b870972e60d
View on Chainz β†—

Height

#442,116

Difficulty

10.352419

Transactions

2

Size

4.32 KB

Version

2

Bits

0a5a3823

Nonce

67,415

Timestamp

3/13/2014, 2:27:45 PM

Confirmations

6,384,642

Mined by

⛏️ P2SHAJhr6wenio3Wgde7Dyqy4HhXVhDAq9Tpnu

Merkle Root

b6eff4241a2e396b2e0c2be5a4f410bd5afcf064a3be9e1dc74f4d45f10af434
Transactions (2)
Coinbaseb9707b68507b75…e05e24e9d08d49
1 in β†’ 1 out9.3700 XPM109 B
AJhr6wen…DAq9Tpnu
726bcad714d2cc…512fb989058ade
28 in β†’ 2 out234.1531 XPM4.12 KB
AQJPJmo6…UN3CdMcMAPhZbt91…ERWP9zpq
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.

2.048 Γ— 10⁹⁡(96-digit number)
20480906913686091532…98751654476628883199
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
2.048 Γ— 10⁹⁡(96-digit number)
20480906913686091532…98751654476628883199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.096 Γ— 10⁹⁡(96-digit number)
40961813827372183064…97503308953257766399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.192 Γ— 10⁹⁡(96-digit number)
81923627654744366129…95006617906515532799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.638 Γ— 10⁹⁢(97-digit number)
16384725530948873225…90013235813031065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.276 Γ— 10⁹⁢(97-digit number)
32769451061897746451…80026471626062131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.553 Γ— 10⁹⁢(97-digit number)
65538902123795492903…60052943252124262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁷(98-digit number)
13107780424759098580…20105886504248524799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.621 Γ— 10⁹⁷(98-digit number)
26215560849518197161…40211773008497049599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.243 Γ— 10⁹⁷(98-digit number)
52431121699036394322…80423546016994099199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁸(99-digit number)
10486224339807278864…60847092033988198399
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:57,858,223 XPMΒ·at block #6,826,757 Β· updates every 60s
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