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Block #2,719,785

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/24/2018, 8:45:02 PM Β· Difficulty 11.6129 Β· 4,122,175 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1a006c5dfda3a3acf3aa0f94bfccdf312ebe62c5565fe3a608cac6cd8cd86ed
View on Chainz β†—

Height

#2,719,785

Difficulty

11.612901

Transactions

1

Size

201 B

Version

2

Bits

0b9ce71a

Nonce

1,121,557,936

Timestamp

6/24/2018, 8:45:02 PM

Confirmations

4,122,175

Mined by

⛏️ P2SHAcNnwx5N2oQHLXU1HxPvAnB57KP6bDDAqD

Merkle Root

7047411f25fcab96038424d49df741bb6ecf1f638bb8bd5b89c621850de07a0c
Transactions (1)
Coinbase7047411f25fcab…c621850de07a0c
1 in β†’ 1 out7.4000 XPM110 B
AcNnwx5N…P6bDDAqD
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.

7.109 Γ— 10⁹⁢(97-digit number)
71094629670183274136…40074399863373004799
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
7.109 Γ— 10⁹⁢(97-digit number)
71094629670183274136…40074399863373004799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.421 Γ— 10⁹⁷(98-digit number)
14218925934036654827…80148799726746009599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.843 Γ— 10⁹⁷(98-digit number)
28437851868073309654…60297599453492019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.687 Γ— 10⁹⁷(98-digit number)
56875703736146619309…20595198906984038399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.137 Γ— 10⁹⁸(99-digit number)
11375140747229323861…41190397813968076799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.275 Γ— 10⁹⁸(99-digit number)
22750281494458647723…82380795627936153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.550 Γ— 10⁹⁸(99-digit number)
45500562988917295447…64761591255872307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.100 Γ— 10⁹⁸(99-digit number)
91001125977834590894…29523182511744614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.820 Γ— 10⁹⁹(100-digit number)
18200225195566918178…59046365023489228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.640 Γ— 10⁹⁹(100-digit number)
36400450391133836357…18092730046978457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.280 Γ— 10⁹⁹(100-digit number)
72800900782267672715…36185460093956915199
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:57,980,061 XPMΒ·at block #6,841,959 Β· updates every 60s
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