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Block #2,867,211

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/4/2018, 6:26:54 PM Β· Difficulty 11.6673 Β· 3,966,711 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7295f30fdbdfec52033e6d9254cfee50f239b3279d10ca9edb082c338ad9366c
View on Chainz β†—

Height

#2,867,211

Difficulty

11.667310

Transactions

2

Size

542 B

Version

2

Bits

0baad4ce

Nonce

686,529,130

Timestamp

10/4/2018, 6:26:54 PM

Confirmations

3,966,711

Mined by

⛏️ P2SHAYztvLQFykjAjRxrtncyvJafhjyzVG5DCZ

Merkle Root

b270a134a0ec9d24a3619d31e5bab81fd0992a880df281e1d9ecb5a002656cf9
Transactions (2)
Coinbase0d5f748d882bf7…352f3152d78bd7
1 in β†’ 1 out7.3400 XPM110 B
AYztvLQF…yzVG5DCZ
7167f6ecfc9db6…146fba122c949e
2 in β†’ 2 out10.1675 XPM342 B
AKg1ZDPd…oM9Ui2azAXCGoVa4…4e7qSiHM
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.

1.314 Γ— 10⁹⁴(95-digit number)
13141596022399599207…86431403462766808579
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
1.314 Γ— 10⁹⁴(95-digit number)
13141596022399599207…86431403462766808579
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.628 Γ— 10⁹⁴(95-digit number)
26283192044799198414…72862806925533617159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.256 Γ— 10⁹⁴(95-digit number)
52566384089598396829…45725613851067234319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.051 Γ— 10⁹⁡(96-digit number)
10513276817919679365…91451227702134468639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.102 Γ— 10⁹⁡(96-digit number)
21026553635839358731…82902455404268937279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.205 Γ— 10⁹⁡(96-digit number)
42053107271678717463…65804910808537874559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.410 Γ— 10⁹⁡(96-digit number)
84106214543357434927…31609821617075749119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.682 Γ— 10⁹⁢(97-digit number)
16821242908671486985…63219643234151498239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.364 Γ— 10⁹⁢(97-digit number)
33642485817342973971…26439286468302996479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.728 Γ— 10⁹⁢(97-digit number)
67284971634685947942…52878572936605992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.345 Γ— 10⁹⁷(98-digit number)
13456994326937189588…05757145873211985919
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:57,915,603 XPMΒ·at block #6,833,921 Β· updates every 60s
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