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Block #2,639,912

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 7:54:11 PM Β· Difficulty 11.5583 Β· 4,201,180 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cfba23ec11deea96bb26dd85a03ea12892ef78b046359b9ba775cf59a7894c09
View on Chainz β†—

Height

#2,639,912

Difficulty

11.558288

Transactions

1

Size

200 B

Version

2

Bits

0b8eebf1

Nonce

379,274,658

Timestamp

4/30/2018, 7:54:11 PM

Confirmations

4,201,180

Mined by

⛏️ P2SHAYNnhWjiYEYXyVEbufLDsuFLKpkEvGzZQS

Merkle Root

eddc2a0708501144d7278fabb16cea86daa3878df5a81023efd52992d509fcd2
Transactions (1)
Coinbaseeddc2a07085011…d52992d509fcd2
1 in β†’ 1 out7.4700 XPM110 B
AYNnhWji…kEvGzZQS
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.

4.812 Γ— 10⁹⁡(96-digit number)
48127989149476631087…22240801174704156159
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
4.812 Γ— 10⁹⁡(96-digit number)
48127989149476631087…22240801174704156159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.625 Γ— 10⁹⁡(96-digit number)
96255978298953262174…44481602349408312319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.925 Γ— 10⁹⁢(97-digit number)
19251195659790652434…88963204698816624639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.850 Γ— 10⁹⁢(97-digit number)
38502391319581304869…77926409397633249279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.700 Γ— 10⁹⁢(97-digit number)
77004782639162609739…55852818795266498559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁷(98-digit number)
15400956527832521947…11705637590532997119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.080 Γ— 10⁹⁷(98-digit number)
30801913055665043895…23411275181065994239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.160 Γ— 10⁹⁷(98-digit number)
61603826111330087791…46822550362131988479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁸(99-digit number)
12320765222266017558…93645100724263976959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.464 Γ— 10⁹⁸(99-digit number)
24641530444532035116…87290201448527953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.928 Γ— 10⁹⁸(99-digit number)
49283060889064070233…74580402897055907839
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:57,973,100 XPMΒ·at block #6,841,091 Β· updates every 60s
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