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Block #1,428,641

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/26/2016, 8:05:52 AM Β· Difficulty 10.7426 Β· 5,381,211 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
26dcaa984ddb31375e94ae5ac23cca45f29c49bbba2fa900a59fb8030aac76e2
View on Chainz β†—

Height

#1,428,641

Difficulty

10.742610

Transactions

2

Size

16.75 KB

Version

2

Bits

0abe1ba9

Nonce

172,796,981

Timestamp

1/26/2016, 8:05:52 AM

Confirmations

5,381,211

Mined by

⛏️ P2SHAar5f4qaBK8a6TRHABg63ifz7xudGEoNrc

Merkle Root

4095adc5bc81f7c366c5c3c07d8bdd437754e09402c0c18de9517e851b92036e
Transactions (2)
Coinbase019c59203c4f24…7119f1711df436
1 in β†’ 1 out8.8200 XPM110 B
Aar5f4qa…udGEoNrc
96eedf86ba1864…188dd0c8e0f7e8
114 in β†’ 2 out3179.1156 XPM16.56 KB
AbZtrUSv…B4zGCFDYATJeka45…7yXJQkRn
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.

1.718 Γ— 10⁹⁴(95-digit number)
17183993451300544080…57352046508216752639
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
1.718 Γ— 10⁹⁴(95-digit number)
17183993451300544080…57352046508216752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.436 Γ— 10⁹⁴(95-digit number)
34367986902601088161…14704093016433505279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.873 Γ— 10⁹⁴(95-digit number)
68735973805202176323…29408186032867010559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.374 Γ— 10⁹⁡(96-digit number)
13747194761040435264…58816372065734021119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.749 Γ— 10⁹⁡(96-digit number)
27494389522080870529…17632744131468042239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.498 Γ— 10⁹⁡(96-digit number)
54988779044161741058…35265488262936084479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.099 Γ— 10⁹⁢(97-digit number)
10997755808832348211…70530976525872168959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.199 Γ— 10⁹⁢(97-digit number)
21995511617664696423…41061953051744337919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.399 Γ— 10⁹⁢(97-digit number)
43991023235329392847…82123906103488675839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.798 Γ— 10⁹⁢(97-digit number)
87982046470658785694…64247812206977351679
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:57,722,903 XPMΒ·at block #6,809,851 Β· updates every 60s
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