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Block #1,181,719

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/3/2015, 4:33:53 PM Β· Difficulty 10.9180 Β· 5,645,353 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fc45e179b5b2c521f63b84d6b5c1a796a7be42887608ca6570e99766aed3005b
View on Chainz β†—

Height

#1,181,719

Difficulty

10.918008

Transactions

1

Size

199 B

Version

2

Bits

0aeb0298

Nonce

20,780

Timestamp

8/3/2015, 4:33:53 PM

Confirmations

5,645,353

Mined by

⛏️ P2SHARaPyHgjo2zpePAfC2xk8aeQGMnA9veLYH

Merkle Root

ffbe58b68c446aa7e699b876ca3c21c1bb8a59cb20f5ec1151d1bcce23ac9c15
Transactions (1)
Coinbaseffbe58b68c446a…d1bcce23ac9c15
1 in β†’ 1 out8.3800 XPM109 B
ARaPyHgj…nA9veLYH
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.

2.128 Γ— 10⁹⁡(96-digit number)
21288377238591205868…67168232265397762241
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.128 Γ— 10⁹⁡(96-digit number)
21288377238591205868…67168232265397762241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.257 Γ— 10⁹⁡(96-digit number)
42576754477182411737…34336464530795524481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.515 Γ— 10⁹⁡(96-digit number)
85153508954364823474…68672929061591048961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.703 Γ— 10⁹⁢(97-digit number)
17030701790872964694…37345858123182097921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.406 Γ— 10⁹⁢(97-digit number)
34061403581745929389…74691716246364195841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.812 Γ— 10⁹⁢(97-digit number)
68122807163491858779…49383432492728391681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.362 Γ— 10⁹⁷(98-digit number)
13624561432698371755…98766864985456783361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.724 Γ— 10⁹⁷(98-digit number)
27249122865396743511…97533729970913566721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.449 Γ— 10⁹⁷(98-digit number)
54498245730793487023…95067459941827133441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.089 Γ— 10⁹⁸(99-digit number)
10899649146158697404…90134919883654266881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.179 Γ— 10⁹⁸(99-digit number)
21799298292317394809…80269839767308533761
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,860,759 XPMΒ·at block #6,827,071 Β· updates every 60s
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