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Block #458,898

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/24/2014, 10:22:27 PM Β· Difficulty 10.4199 Β· 6,344,290 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ad52afb80b0d700f310ff0d7a2d5eb6cf6063a888b39bdcee97a1275bb9d93d0
View on Chainz β†—

Height

#458,898

Difficulty

10.419933

Transactions

1

Size

289 B

Version

2

Bits

0a6b80b7

Nonce

284,478

Timestamp

3/24/2014, 10:22:27 PM

Confirmations

6,344,290

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

d38163531525f8ec4a9db7e0c957d78247b2e01c6bc58fbe0f9c657f8fd7dc04
Transactions (1)
Coinbased38163531525f8…9c657f8fd7dc04
1 in β†’ 4 out9.2000 XPM199 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAa2Amg89…4rjYrsPZAJno7LX2…vo4wdWtY
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.

1.619 Γ— 10⁹⁡(96-digit number)
16190066435028554492…95729675072796027399
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
1.619 Γ— 10⁹⁡(96-digit number)
16190066435028554492…95729675072796027399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.238 Γ— 10⁹⁡(96-digit number)
32380132870057108985…91459350145592054799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.476 Γ— 10⁹⁡(96-digit number)
64760265740114217971…82918700291184109599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.295 Γ— 10⁹⁢(97-digit number)
12952053148022843594…65837400582368219199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.590 Γ— 10⁹⁢(97-digit number)
25904106296045687188…31674801164736438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.180 Γ— 10⁹⁢(97-digit number)
51808212592091374377…63349602329472876799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.036 Γ— 10⁹⁷(98-digit number)
10361642518418274875…26699204658945753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.072 Γ— 10⁹⁷(98-digit number)
20723285036836549750…53398409317891507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.144 Γ— 10⁹⁷(98-digit number)
41446570073673099501…06796818635783014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.289 Γ— 10⁹⁷(98-digit number)
82893140147346199003…13593637271566028799
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:57,669,524 XPMΒ·at block #6,803,187 Β· updates every 60s
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