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Block #2,825,912

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2018, 2:11:29 PM Β· Difficulty 11.7100 Β· 4,018,123 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f0d7033bd05872b94c5eb96c7ed7ba668f58a1475c7868b66ab680704542906
View on Chainz β†—

Height

#2,825,912

Difficulty

11.710036

Transactions

1

Size

201 B

Version

2

Bits

0bb5c4e4

Nonce

1,871,718,315

Timestamp

9/5/2018, 2:11:29 PM

Confirmations

4,018,123

Mined by

⛏️ P2SHAV9ZaL323obsvSNY4zpcavUQrLEcSu2TdB

Merkle Root

f27a017d13fc7ae314dfb7f0a6480bca7985bddc62ae88649cb2749df917012d
Transactions (1)
Coinbasef27a017d13fc7a…b2749df917012d
1 in β†’ 1 out7.2800 XPM110 B
AV9ZaL32…EcSu2TdB
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.

1.518 Γ— 10⁹⁷(98-digit number)
15189244755503416519…34324170154636871679
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
1.518 Γ— 10⁹⁷(98-digit number)
15189244755503416519…34324170154636871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.037 Γ— 10⁹⁷(98-digit number)
30378489511006833039…68648340309273743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.075 Γ— 10⁹⁷(98-digit number)
60756979022013666078…37296680618547486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁸(99-digit number)
12151395804402733215…74593361237094973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁸(99-digit number)
24302791608805466431…49186722474189946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁸(99-digit number)
48605583217610932862…98373444948379893759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.721 Γ— 10⁹⁸(99-digit number)
97211166435221865725…96746889896759787519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁹(100-digit number)
19442233287044373145…93493779793519575039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁹(100-digit number)
38884466574088746290…86987559587039150079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.776 Γ— 10⁹⁹(100-digit number)
77768933148177492580…73975119174078300159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.555 Γ— 10¹⁰⁰(101-digit number)
15553786629635498516…47950238348156600319
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:57,996,657 XPMΒ·at block #6,844,034 Β· updates every 60s
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