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Block #432,728

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/7/2014, 3:01:01 AM Β· Difficulty 10.3396 Β· 6,383,403 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2fd19627fbe2a3580fbfb408c1fb50f6ca3f3473617849f4274e8fd1e6c6b4e6
View on Chainz β†—

Height

#432,728

Difficulty

10.339624

Transactions

1

Size

200 B

Version

2

Bits

0a56f1a1

Nonce

1,296,601

Timestamp

3/7/2014, 3:01:01 AM

Confirmations

6,383,403

Mined by

⛏️ P2SHAFn9NGFUxHjhzH5uQB8RhjVw1CjoLAZ94Q

Merkle Root

f7e82b0810e6636dc16cf3569ecdc2346670080e8adb301d325332c06cb776f9
Transactions (1)
Coinbasef7e82b0810e663…5332c06cb776f9
1 in β†’ 1 out9.3400 XPM109 B
AFn9NGFU…joLAZ94Q
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.

2.801 Γ— 10⁹⁢(97-digit number)
28018380886903076334…53995826922424870399
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
2.801 Γ— 10⁹⁢(97-digit number)
28018380886903076334…53995826922424870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.603 Γ— 10⁹⁢(97-digit number)
56036761773806152668…07991653844849740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.120 Γ— 10⁹⁷(98-digit number)
11207352354761230533…15983307689699481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.241 Γ— 10⁹⁷(98-digit number)
22414704709522461067…31966615379398963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.482 Γ— 10⁹⁷(98-digit number)
44829409419044922134…63933230758797926399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.965 Γ— 10⁹⁷(98-digit number)
89658818838089844269…27866461517595852799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.793 Γ— 10⁹⁸(99-digit number)
17931763767617968853…55732923035191705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.586 Γ— 10⁹⁸(99-digit number)
35863527535235937707…11465846070383411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.172 Γ— 10⁹⁸(99-digit number)
71727055070471875415…22931692140766822399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.434 Γ— 10⁹⁹(100-digit number)
14345411014094375083…45863384281533644799
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:57,773,174 XPMΒ·at block #6,816,130 Β· updates every 60s
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