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Block #2,796,050

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2018, 4:03:13 AM Β· Difficulty 11.6817 Β· 4,046,343 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
daf709032d86369517af0bc93f9c92553c54d185045cf6cf105b80da5b06ae19
View on Chainz β†—

Height

#2,796,050

Difficulty

11.681666

Transactions

1

Size

201 B

Version

2

Bits

0bae81a7

Nonce

624,810,059

Timestamp

8/16/2018, 4:03:13 AM

Confirmations

4,046,343

Mined by

⛏️ P2SHAMHPenthYqmp17ru1HzsxGHd12VvQsqDK6

Merkle Root

425cbda5aa20206fc1fa35a2ece91c8ee5811d0184f70394fefe3c17226ae7c5
Transactions (1)
Coinbase425cbda5aa2020…fe3c17226ae7c5
1 in β†’ 1 out7.3200 XPM110 B
AMHPenth…VvQsqDK6
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.

9.586 Γ— 10⁹⁢(97-digit number)
95863413984702291291…97143684681722572799
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
9.586 Γ— 10⁹⁢(97-digit number)
95863413984702291291…97143684681722572799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.917 Γ— 10⁹⁷(98-digit number)
19172682796940458258…94287369363445145599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.834 Γ— 10⁹⁷(98-digit number)
38345365593880916516…88574738726890291199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.669 Γ— 10⁹⁷(98-digit number)
76690731187761833033…77149477453780582399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.533 Γ— 10⁹⁸(99-digit number)
15338146237552366606…54298954907561164799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.067 Γ— 10⁹⁸(99-digit number)
30676292475104733213…08597909815122329599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.135 Γ— 10⁹⁸(99-digit number)
61352584950209466426…17195819630244659199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁹(100-digit number)
12270516990041893285…34391639260489318399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁹(100-digit number)
24541033980083786570…68783278520978636799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.908 Γ— 10⁹⁹(100-digit number)
49082067960167573141…37566557041957273599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.816 Γ— 10⁹⁹(100-digit number)
98164135920335146282…75133114083914547199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,983,555 XPMΒ·at block #6,842,392 Β· updates every 60s
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