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Block #2,125,795

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/20/2017, 7:39:02 PM Β· Difficulty 10.9191 Β· 4,682,409 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c88a986977e056bc1ed4e4437017efe53a116df569740169f1f70e6ec4700584
View on Chainz β†—

Height

#2,125,795

Difficulty

10.919115

Transactions

2

Size

1.42 KB

Version

2

Bits

0aeb4b26

Nonce

973,532,044

Timestamp

5/20/2017, 7:39:02 PM

Confirmations

4,682,409

Mined by

⛏️ P2SHAeiiQvLx6viBzzpkywPRZfT1A24czFPJVG

Merkle Root

eb43ac3b2f6c1e032f1b2c2f434557080d3838d894032c1e31f94afb8d8b6c02
Transactions (2)
Coinbase6bef83d2b257c0…1b20dba70710d0
1 in β†’ 1 out8.3900 XPM110 B
AeiiQvLx…4czFPJVG
d31ea3c03afb3c…ddb2db6744232a
8 in β†’ 2 out898.2234 XPM1.23 KB
APyJkHS6…Ju9KmdmXAKEVx6dn…YyTwXwyE
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.

3.834 Γ— 10⁹⁴(95-digit number)
38348608998456728134…33078240964143799039
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
3.834 Γ— 10⁹⁴(95-digit number)
38348608998456728134…33078240964143799039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.669 Γ— 10⁹⁴(95-digit number)
76697217996913456269…66156481928287598079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.533 Γ— 10⁹⁡(96-digit number)
15339443599382691253…32312963856575196159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.067 Γ— 10⁹⁡(96-digit number)
30678887198765382507…64625927713150392319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.135 Γ— 10⁹⁡(96-digit number)
61357774397530765015…29251855426300784639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁢(97-digit number)
12271554879506153003…58503710852601569279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁢(97-digit number)
24543109759012306006…17007421705203138559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.908 Γ— 10⁹⁢(97-digit number)
49086219518024612012…34014843410406277119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.817 Γ— 10⁹⁢(97-digit number)
98172439036049224024…68029686820812554239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.963 Γ— 10⁹⁷(98-digit number)
19634487807209844804…36059373641625108479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.926 Γ— 10⁹⁷(98-digit number)
39268975614419689609…72118747283250216959
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:57,709,684 XPMΒ·at block #6,808,203 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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