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Block #2,165,887

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/18/2017, 12:08:22 PM Β· Difficulty 10.8983 Β· 4,661,034 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f7fd9347cef5b86d74880036d58e297fee1ebd4ce10687949bfc1ce06c4b8756
View on Chainz β†—

Height

#2,165,887

Difficulty

10.898276

Transactions

1

Size

200 B

Version

2

Bits

0ae5f56a

Nonce

1,605,628,799

Timestamp

6/18/2017, 12:08:22 PM

Confirmations

4,661,034

Mined by

⛏️ P2SHANYTZw3vQv6Y1J4xqUmckPkWSRPKjR1aaT

Merkle Root

20f0db90b05b0df9043b04cd4c172d16410cf03c81c0ed65a6a7c55e7b31b5c6
Transactions (1)
Coinbase20f0db90b05b0d…a7c55e7b31b5c6
1 in β†’ 1 out8.4100 XPM110 B
ANYTZw3v…PKjR1aaT
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.

2.505 Γ— 10⁹⁡(96-digit number)
25058297744125739321…36922688537357712639
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
2.505 Γ— 10⁹⁡(96-digit number)
25058297744125739321…36922688537357712639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.011 Γ— 10⁹⁡(96-digit number)
50116595488251478642…73845377074715425279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁢(97-digit number)
10023319097650295728…47690754149430850559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.004 Γ— 10⁹⁢(97-digit number)
20046638195300591456…95381508298861701119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.009 Γ— 10⁹⁢(97-digit number)
40093276390601182913…90763016597723402239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.018 Γ— 10⁹⁢(97-digit number)
80186552781202365827…81526033195446804479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.603 Γ— 10⁹⁷(98-digit number)
16037310556240473165…63052066390893608959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.207 Γ— 10⁹⁷(98-digit number)
32074621112480946330…26104132781787217919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.414 Γ— 10⁹⁷(98-digit number)
64149242224961892661…52208265563574435839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.282 Γ— 10⁹⁸(99-digit number)
12829848444992378532…04416531127148871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.565 Γ— 10⁹⁸(99-digit number)
25659696889984757064…08833062254297743359
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:57,859,539 XPMΒ·at block #6,826,920 Β· updates every 60s
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