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Block #2,872,621

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/8/2018, 12:58:34 PM Β· Difficulty 11.6662 Β· 3,961,333 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
acbc52632aa2519ae35e8635f6ed9b6fc9cd6b3db59ffc5ff260135af0a9c1e1
View on Chainz β†—

Height

#2,872,621

Difficulty

11.666165

Transactions

1

Size

200 B

Version

2

Bits

0baa89cc

Nonce

545,562,150

Timestamp

10/8/2018, 12:58:34 PM

Confirmations

3,961,333

Mined by

⛏️ P2SHAPeVLFNJk41VyozKWSDZ5a7RUdY3cp5kZw

Merkle Root

0c0fe29eede18a300ec306a2d154558c19b9b47bb8aefdca8f57e17154bb3934
Transactions (1)
Coinbase0c0fe29eede18a…57e17154bb3934
1 in β†’ 1 out7.3400 XPM110 B
APeVLFNJ…Y3cp5kZw
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.

2.704 Γ— 10⁹⁴(95-digit number)
27048126050581300296…05445956653195631039
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
2.704 Γ— 10⁹⁴(95-digit number)
27048126050581300296…05445956653195631039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.409 Γ— 10⁹⁴(95-digit number)
54096252101162600593…10891913306391262079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁡(96-digit number)
10819250420232520118…21783826612782524159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.163 Γ— 10⁹⁡(96-digit number)
21638500840465040237…43567653225565048319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.327 Γ— 10⁹⁡(96-digit number)
43277001680930080474…87135306451130096639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.655 Γ— 10⁹⁡(96-digit number)
86554003361860160949…74270612902260193279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.731 Γ— 10⁹⁢(97-digit number)
17310800672372032189…48541225804520386559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.462 Γ— 10⁹⁢(97-digit number)
34621601344744064379…97082451609040773119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.924 Γ— 10⁹⁢(97-digit number)
69243202689488128759…94164903218081546239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.384 Γ— 10⁹⁷(98-digit number)
13848640537897625751…88329806436163092479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.769 Γ— 10⁹⁷(98-digit number)
27697281075795251503…76659612872326184959
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:57,915,862 XPMΒ·at block #6,833,953 Β· updates every 60s
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