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Block #2,077,195

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/19/2017, 5:17:03 AM Β· Difficulty 10.8484 Β· 4,765,669 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
62ff31871aa2424366d077e1f71d38db1b4fda22a68d3ab227aa79a8efaea649
View on Chainz β†—

Height

#2,077,195

Difficulty

10.848354

Transactions

1

Size

200 B

Version

2

Bits

0ad92db4

Nonce

368,726,883

Timestamp

4/19/2017, 5:17:03 AM

Confirmations

4,765,669

Mined by

⛏️ P2SHAbK4PmB2o7RMFgjga8MPKaN8U3PKmkgLbm

Merkle Root

d4a06cbcc3f25303168feb03d7c490c36ff8f3cc8ec80bf75725b11f02eb3453
Transactions (1)
Coinbased4a06cbcc3f253…25b11f02eb3453
1 in β†’ 1 out8.4800 XPM110 B
AbK4PmB2…PKmkgLbm
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.

3.661 Γ— 10⁹⁡(96-digit number)
36618989262964156840…04816913458422030719
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
3.661 Γ— 10⁹⁡(96-digit number)
36618989262964156840…04816913458422030719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.323 Γ— 10⁹⁡(96-digit number)
73237978525928313680…09633826916844061439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.464 Γ— 10⁹⁢(97-digit number)
14647595705185662736…19267653833688122879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.929 Γ— 10⁹⁢(97-digit number)
29295191410371325472…38535307667376245759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.859 Γ— 10⁹⁢(97-digit number)
58590382820742650944…77070615334752491519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.171 Γ— 10⁹⁷(98-digit number)
11718076564148530188…54141230669504983039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.343 Γ— 10⁹⁷(98-digit number)
23436153128297060377…08282461339009966079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.687 Γ— 10⁹⁷(98-digit number)
46872306256594120755…16564922678019932159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.374 Γ— 10⁹⁷(98-digit number)
93744612513188241511…33129845356039864319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.874 Γ— 10⁹⁸(99-digit number)
18748922502637648302…66259690712079728639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,987,258 XPMΒ·at block #6,842,863 Β· updates every 60s
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