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Block #2,660,059

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/14/2018, 3:02:56 AM Β· Difficulty 11.6385 Β· 4,184,500 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3376784a9c0c3a9156e9995c367adffda5cd076469cd011a6912d7777d295b5d
View on Chainz β†—

Height

#2,660,059

Difficulty

11.638550

Transactions

1

Size

201 B

Version

2

Bits

0ba37800

Nonce

1,377,692,930

Timestamp

5/14/2018, 3:02:56 AM

Confirmations

4,184,500

Mined by

⛏️ P2SHAZfrtCf3x2rwFRmCmL2srwpXGqfGtZKE2g

Merkle Root

f7396bca51df0625078071fa995d55c50ebff399f840b4cb2a20f5f4ddc36847
Transactions (1)
Coinbasef7396bca51df06…20f5f4ddc36847
1 in β†’ 1 out7.3700 XPM110 B
AZfrtCf3…fGtZKE2g
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.

1.124 Γ— 10⁹⁸(99-digit number)
11245732198778441765…45279583217238507519
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
1.124 Γ— 10⁹⁸(99-digit number)
11245732198778441765…45279583217238507519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.249 Γ— 10⁹⁸(99-digit number)
22491464397556883530…90559166434477015039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.498 Γ— 10⁹⁸(99-digit number)
44982928795113767060…81118332868954030079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.996 Γ— 10⁹⁸(99-digit number)
89965857590227534121…62236665737908060159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁹(100-digit number)
17993171518045506824…24473331475816120319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.598 Γ— 10⁹⁹(100-digit number)
35986343036091013648…48946662951632240639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.197 Γ— 10⁹⁹(100-digit number)
71972686072182027297…97893325903264481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.439 Γ— 10¹⁰⁰(101-digit number)
14394537214436405459…95786651806528962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.878 Γ— 10¹⁰⁰(101-digit number)
28789074428872810918…91573303613057925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.757 Γ— 10¹⁰⁰(101-digit number)
57578148857745621837…83146607226115850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.151 Γ— 10¹⁰¹(102-digit number)
11515629771549124367…66293214452231700479
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:58,000,874 XPMΒ·at block #6,844,558 Β· updates every 60s
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