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Block #3,223,885

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2019, 6:46:16 PM Β· Difficulty 11.0150 Β· 3,617,668 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2939797220329a80577a2a3d36e823f6e31b76072dc7fa3daf0f7266f14772a1
View on Chainz β†—

Height

#3,223,885

Difficulty

11.014993

Transactions

2

Size

575 B

Version

2

Bits

0b03d690

Nonce

1,688,773,776

Timestamp

6/13/2019, 6:46:16 PM

Confirmations

3,617,668

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

68898dc7e5843bfd9fb2a60438cf2f8b05098af17b6817e940401b845d77af14
Transactions (2)
Coinbase26861454580714…0fee97c675abd5
1 in β†’ 1 out8.2400 XPM110 B
ARbm48qR…9xQc8DBX
27203d877d596d…9301b291081559
2 in β†’ 2 out294.0502 XPM375 B
AeTHTL7A…vT1872bkAFxcdHBJ…9mzhd1pF
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.

1.476 Γ— 10⁹⁴(95-digit number)
14760845116207034484…38981606551726377999
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
1.476 Γ— 10⁹⁴(95-digit number)
14760845116207034484…38981606551726377999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.952 Γ— 10⁹⁴(95-digit number)
29521690232414068968…77963213103452755999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.904 Γ— 10⁹⁴(95-digit number)
59043380464828137937…55926426206905511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁡(96-digit number)
11808676092965627587…11852852413811023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.361 Γ— 10⁹⁡(96-digit number)
23617352185931255175…23705704827622047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.723 Γ— 10⁹⁡(96-digit number)
47234704371862510350…47411409655244095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.446 Γ— 10⁹⁡(96-digit number)
94469408743725020700…94822819310488191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.889 Γ— 10⁹⁢(97-digit number)
18893881748745004140…89645638620976383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.778 Γ— 10⁹⁢(97-digit number)
37787763497490008280…79291277241952767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.557 Γ— 10⁹⁢(97-digit number)
75575526994980016560…58582554483905535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.511 Γ— 10⁹⁷(98-digit number)
15115105398996003312…17165108967811071999
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:57,976,808 XPMΒ·at block #6,841,552 Β· updates every 60s
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