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Block #358,025

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2014, 7:10:48 PM Β· Difficulty 10.3899 Β· 6,456,955 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b0a670c572125673d76ff77851b19f3730f02593407a5af3f66983102448502b
View on Chainz β†—

Height

#358,025

Difficulty

10.389860

Transactions

2

Size

394 B

Version

2

Bits

0a63cdda

Nonce

646,783

Timestamp

1/13/2014, 7:10:48 PM

Confirmations

6,456,955

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

764998745eb6e32041472eb101ed75f3f14d9e11831573a14e8a160c150e7eed
Transactions (2)
Coinbase111a8ac3a208c0…306df273f96146
1 in β†’ 1 out9.2600 XPM110 B
AeKNrjNj…1NEq95Ta
30ce8df143809b…e4a51d6124b3ba
1 in β†’ 1 out3.0964 XPM193 B
AH8DMgW2…Fs4tzdjQ
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.

3.217 Γ— 10⁹⁷(98-digit number)
32170590194043111820…70110311876877363099
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
3.217 Γ— 10⁹⁷(98-digit number)
32170590194043111820…70110311876877363099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.434 Γ— 10⁹⁷(98-digit number)
64341180388086223640…40220623753754726199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.286 Γ— 10⁹⁸(99-digit number)
12868236077617244728…80441247507509452399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.573 Γ— 10⁹⁸(99-digit number)
25736472155234489456…60882495015018904799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.147 Γ— 10⁹⁸(99-digit number)
51472944310468978912…21764990030037809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.029 Γ— 10⁹⁹(100-digit number)
10294588862093795782…43529980060075619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.058 Γ— 10⁹⁹(100-digit number)
20589177724187591565…87059960120151238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.117 Γ— 10⁹⁹(100-digit number)
41178355448375183130…74119920240302476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.235 Γ— 10⁹⁹(100-digit number)
82356710896750366260…48239840480604953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.647 Γ— 10¹⁰⁰(101-digit number)
16471342179350073252…96479680961209907199
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:57,763,927 XPMΒ·at block #6,814,979 Β· updates every 60s
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