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Block #2,145,172

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2017, 11:03:17 AM Β· Difficulty 10.8872 Β· 4,682,184 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac989a05d5e0e3d4cdee3d4d3d4f937adc03ec8bf4ab8dd6d79570ecae01f054
View on Chainz β†—

Height

#2,145,172

Difficulty

10.887169

Transactions

1

Size

200 B

Version

2

Bits

0ae31d85

Nonce

64,115,601

Timestamp

6/4/2017, 11:03:17 AM

Confirmations

4,682,184

Mined by

⛏️ P2SHAVFkVK4KnVdtjH1YBDNsdzTLuhmAKn2zL5

Merkle Root

c4f861193487c23565a7c9126aecbe16b1b935424085b174542571f2aec62d53
Transactions (1)
Coinbasec4f861193487c2…2571f2aec62d53
1 in β†’ 1 out8.4200 XPM110 B
AVFkVK4K…mAKn2zL5
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.

5.333 Γ— 10⁹⁴(95-digit number)
53332595085464547372…22925272908593745641
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
5.333 Γ— 10⁹⁴(95-digit number)
53332595085464547372…22925272908593745641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.066 Γ— 10⁹⁡(96-digit number)
10666519017092909474…45850545817187491281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.133 Γ— 10⁹⁡(96-digit number)
21333038034185818948…91701091634374982561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.266 Γ— 10⁹⁡(96-digit number)
42666076068371637897…83402183268749965121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.533 Γ— 10⁹⁡(96-digit number)
85332152136743275795…66804366537499930241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.706 Γ— 10⁹⁢(97-digit number)
17066430427348655159…33608733074999860481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.413 Γ— 10⁹⁢(97-digit number)
34132860854697310318…67217466149999720961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.826 Γ— 10⁹⁢(97-digit number)
68265721709394620636…34434932299999441921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.365 Γ— 10⁹⁷(98-digit number)
13653144341878924127…68869864599998883841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.730 Γ— 10⁹⁷(98-digit number)
27306288683757848254…37739729199997767681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.461 Γ— 10⁹⁷(98-digit number)
54612577367515696509…75479458399995535361
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:57,862,946 XPMΒ·at block #6,827,355 Β· updates every 60s
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