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Block #1,420,035

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/19/2016, 3:34:49 PM Β· Difficulty 10.7897 Β· 5,419,352 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98079cc4878c041068afdbba3aa9444e85758ec6b39c128de8d51593226f3db4
View on Chainz β†—

Height

#1,420,035

Difficulty

10.789719

Transactions

2

Size

3.74 KB

Version

2

Bits

0aca2b0c

Nonce

1,075,254,306

Timestamp

1/19/2016, 3:34:49 PM

Confirmations

5,419,352

Mined by

⛏️ P2SHARaj5TaYeG2S3eVvhMsphhA5yF1vi9Gw67

Merkle Root

6b77a5da45b0feff13c82a0b78bad6fc3c2d276fb3aa81b0132f8e36400bb1db
Transactions (2)
Coinbase61167cac1d89a8…bce8d26f1262e5
1 in β†’ 1 out8.6200 XPM109 B
ARaj5TaY…1vi9Gw67
c751a7a63fe767…7d848e26607dd2
24 in β†’ 2 out12.2795 XPM3.54 KB
AULJqW7T…TL2PLdFsAcXXohiP…q4T24mCs
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.

1.663 Γ— 10⁹⁷(98-digit number)
16639915743208821549…26125731243796725759
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
1.663 Γ— 10⁹⁷(98-digit number)
16639915743208821549…26125731243796725759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.327 Γ— 10⁹⁷(98-digit number)
33279831486417643098…52251462487593451519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.655 Γ— 10⁹⁷(98-digit number)
66559662972835286196…04502924975186903039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.331 Γ— 10⁹⁸(99-digit number)
13311932594567057239…09005849950373806079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.662 Γ— 10⁹⁸(99-digit number)
26623865189134114478…18011699900747612159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.324 Γ— 10⁹⁸(99-digit number)
53247730378268228957…36023399801495224319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.064 Γ— 10⁹⁹(100-digit number)
10649546075653645791…72046799602990448639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.129 Γ— 10⁹⁹(100-digit number)
21299092151307291582…44093599205980897279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.259 Γ— 10⁹⁹(100-digit number)
42598184302614583165…88187198411961794559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.519 Γ— 10⁹⁹(100-digit number)
85196368605229166331…76374396823923589119
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:57,959,380 XPMΒ·at block #6,839,386 Β· updates every 60s
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