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Block #2,643,874

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 6:34:54 AM Β· Difficulty 11.6960 Β· 4,194,822 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
03d2f606aed50de6a116d4a369197ce1ff63cd35bad3841cad49c87ef15d8485
View on Chainz β†—

Height

#2,643,874

Difficulty

11.696001

Transactions

1

Size

200 B

Version

2

Bits

0bb22d24

Nonce

834,324,419

Timestamp

5/2/2018, 6:34:54 AM

Confirmations

4,194,822

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

cec63f630848e8f03b43708129ff0fe137da1dff58685b7bdf27794123e717aa
Transactions (1)
Coinbasecec63f630848e8…27794123e717aa
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

7.608 Γ— 10⁹³(94-digit number)
76085796101742417901…15070668710809043919
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
7.608 Γ— 10⁹³(94-digit number)
76085796101742417901…15070668710809043919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.521 Γ— 10⁹⁴(95-digit number)
15217159220348483580…30141337421618087839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.043 Γ— 10⁹⁴(95-digit number)
30434318440696967160…60282674843236175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.086 Γ— 10⁹⁴(95-digit number)
60868636881393934320…20565349686472351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁡(96-digit number)
12173727376278786864…41130699372944702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.434 Γ— 10⁹⁡(96-digit number)
24347454752557573728…82261398745889405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.869 Γ— 10⁹⁡(96-digit number)
48694909505115147456…64522797491778810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.738 Γ— 10⁹⁡(96-digit number)
97389819010230294913…29045594983557621759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁢(97-digit number)
19477963802046058982…58091189967115243519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.895 Γ— 10⁹⁢(97-digit number)
38955927604092117965…16182379934230487039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.791 Γ— 10⁹⁢(97-digit number)
77911855208184235930…32364759868460974079
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:57,953,832 XPMΒ·at block #6,838,695 Β· updates every 60s
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