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Block #2,785,620

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/9/2018, 12:37:12 AM Β· Difficulty 11.6722 Β· 4,055,887 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c86258cb92d1b585ec126527f5ef02529bd97266c1fe38f2ed6a7ce6335e2a83
View on Chainz β†—

Height

#2,785,620

Difficulty

11.672178

Transactions

1

Size

200 B

Version

2

Bits

0bac13d4

Nonce

1,787,122,216

Timestamp

8/9/2018, 12:37:12 AM

Confirmations

4,055,887

Mined by

⛏️ P2SHAWoWNH2TEPx17tGPAveXtCQNtNVT7HkjZz

Merkle Root

e6f077fa676dd63beb2be49145d1867c129b2af649cdd66087d4a1511838e04c
Transactions (1)
Coinbasee6f077fa676dd6…d4a1511838e04c
1 in β†’ 1 out7.3300 XPM110 B
AWoWNH2T…VT7HkjZz
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.

2.181 Γ— 10⁹⁴(95-digit number)
21818883455763497037…73246507404952719199
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
2.181 Γ— 10⁹⁴(95-digit number)
21818883455763497037…73246507404952719199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.363 Γ— 10⁹⁴(95-digit number)
43637766911526994075…46493014809905438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.727 Γ— 10⁹⁴(95-digit number)
87275533823053988151…92986029619810876799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.745 Γ— 10⁹⁡(96-digit number)
17455106764610797630…85972059239621753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.491 Γ— 10⁹⁡(96-digit number)
34910213529221595260…71944118479243507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.982 Γ— 10⁹⁡(96-digit number)
69820427058443190521…43888236958487014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.396 Γ— 10⁹⁢(97-digit number)
13964085411688638104…87776473916974028799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.792 Γ— 10⁹⁢(97-digit number)
27928170823377276208…75552947833948057599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.585 Γ— 10⁹⁢(97-digit number)
55856341646754552417…51105895667896115199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.117 Γ— 10⁹⁷(98-digit number)
11171268329350910483…02211791335792230399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.234 Γ— 10⁹⁷(98-digit number)
22342536658701820966…04423582671584460799
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:57,976,435 XPMΒ·at block #6,841,506 Β· updates every 60s
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