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Block #2,795,614

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/15/2018, 9:16:16 PM Β· Difficulty 11.6799 Β· 4,045,011 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6fdf6178e16b1f218d138b84df0d7b494c0887fb160624f16ebe25058b49c28
View on Chainz β†—

Height

#2,795,614

Difficulty

11.679879

Transactions

1

Size

200 B

Version

2

Bits

0bae0c86

Nonce

497,549,423

Timestamp

8/15/2018, 9:16:16 PM

Confirmations

4,045,011

Mined by

⛏️ P2SHAd7s4bdUFNibVe4FqA1NRTTQ1Ct8NcM9ur

Merkle Root

2fcd4f017ffc60d6d98a73cd349ed8869b75057e6fddb57855b5647eb2a593c2
Transactions (1)
Coinbase2fcd4f017ffc60…b5647eb2a593c2
1 in β†’ 1 out7.3200 XPM110 B
Ad7s4bdU…t8NcM9ur
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.

1.858 Γ— 10⁹⁴(95-digit number)
18588102055025468544…76270319455916960399
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
1.858 Γ— 10⁹⁴(95-digit number)
18588102055025468544…76270319455916960399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.717 Γ— 10⁹⁴(95-digit number)
37176204110050937088…52540638911833920799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.435 Γ— 10⁹⁴(95-digit number)
74352408220101874176…05081277823667841599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.487 Γ— 10⁹⁡(96-digit number)
14870481644020374835…10162555647335683199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.974 Γ— 10⁹⁡(96-digit number)
29740963288040749670…20325111294671366399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.948 Γ— 10⁹⁡(96-digit number)
59481926576081499340…40650222589342732799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.189 Γ— 10⁹⁢(97-digit number)
11896385315216299868…81300445178685465599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.379 Γ— 10⁹⁢(97-digit number)
23792770630432599736…62600890357370931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.758 Γ— 10⁹⁢(97-digit number)
47585541260865199472…25201780714741862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.517 Γ— 10⁹⁢(97-digit number)
95171082521730398945…50403561429483724799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁷(98-digit number)
19034216504346079789…00807122858967449599
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:57,969,340 XPMΒ·at block #6,840,624 Β· updates every 60s
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