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Block #2,803,996

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2018, 8:31:27 PM Β· Difficulty 11.6663 Β· 4,036,176 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
387297a2d689e236b73d5d0ea7dfc6debf343917713ffec8a55b188c7ab2217c
View on Chainz β†—

Height

#2,803,996

Difficulty

11.666282

Transactions

1

Size

201 B

Version

2

Bits

0baa916d

Nonce

871,594,282

Timestamp

8/21/2018, 8:31:27 PM

Confirmations

4,036,176

Mined by

⛏️ P2SHALRbRUA8YSLdd1YqVbJcPEPrrU868J2Mr3

Merkle Root

95ecbc62cfdc281663badcac065c35d67547e1d31bc2c0c4593e5d2f899c54dc
Transactions (1)
Coinbase95ecbc62cfdc28…3e5d2f899c54dc
1 in β†’ 1 out7.3400 XPM110 B
ALRbRUA8…868J2Mr3
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.

6.571 Γ— 10⁹⁡(96-digit number)
65716006830554450398…31779624461212399039
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
6.571 Γ— 10⁹⁡(96-digit number)
65716006830554450398…31779624461212399039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.314 Γ— 10⁹⁢(97-digit number)
13143201366110890079…63559248922424798079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.628 Γ— 10⁹⁢(97-digit number)
26286402732221780159…27118497844849596159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.257 Γ— 10⁹⁢(97-digit number)
52572805464443560319…54236995689699192319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.051 Γ— 10⁹⁷(98-digit number)
10514561092888712063…08473991379398384639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.102 Γ— 10⁹⁷(98-digit number)
21029122185777424127…16947982758796769279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.205 Γ— 10⁹⁷(98-digit number)
42058244371554848255…33895965517593538559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.411 Γ— 10⁹⁷(98-digit number)
84116488743109696510…67791931035187077119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.682 Γ— 10⁹⁸(99-digit number)
16823297748621939302…35583862070374154239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.364 Γ— 10⁹⁸(99-digit number)
33646595497243878604…71167724140748308479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.729 Γ— 10⁹⁸(99-digit number)
67293190994487757208…42335448281496616959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.345 Γ— 10⁹⁹(100-digit number)
13458638198897551441…84670896562993233919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,965,697 XPMΒ·at block #6,840,171 Β· updates every 60s
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