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Block #3,105,020

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/22/2019, 11:39:43 AM Β· Difficulty 11.1999 Β· 3,728,069 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4627839d138e3841b04da44417d04cb2fcbb918cebe506b2684e96e874f2de42
View on Chainz β†—

Height

#3,105,020

Difficulty

11.199850

Transactions

2

Size

1.72 KB

Version

2

Bits

0b332963

Nonce

190,818,373

Timestamp

3/22/2019, 11:39:43 AM

Confirmations

3,728,069

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

7a9285de2d9ed6ef4778849294ac9781d79d50592993629dec2fa66a9a70527c
Transactions (2)
Coinbase1b68605408c0b0…6774153f7a3735
1 in β†’ 1 out7.9800 XPM110 B
ARbm48qR…9xQc8DBX
91073440a45c12…c4512d1d32a0da
10 in β†’ 2 out81.8144 XPM1.52 KB
APGM3HCy…NvJoz5XLAH8H4ppQ…uayteYn3
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.

4.456 Γ— 10⁹⁴(95-digit number)
44564116401553822902…69288448965096542599
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
4.456 Γ— 10⁹⁴(95-digit number)
44564116401553822902…69288448965096542599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.912 Γ— 10⁹⁴(95-digit number)
89128232803107645805…38576897930193085199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.782 Γ— 10⁹⁡(96-digit number)
17825646560621529161…77153795860386170399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.565 Γ— 10⁹⁡(96-digit number)
35651293121243058322…54307591720772340799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.130 Γ— 10⁹⁡(96-digit number)
71302586242486116644…08615183441544681599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.426 Γ— 10⁹⁢(97-digit number)
14260517248497223328…17230366883089363199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.852 Γ— 10⁹⁢(97-digit number)
28521034496994446657…34460733766178726399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.704 Γ— 10⁹⁢(97-digit number)
57042068993988893315…68921467532357452799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.140 Γ— 10⁹⁷(98-digit number)
11408413798797778663…37842935064714905599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.281 Γ— 10⁹⁷(98-digit number)
22816827597595557326…75685870129429811199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.563 Γ— 10⁹⁷(98-digit number)
45633655195191114652…51371740258859622399
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:57,908,887 XPMΒ·at block #6,833,088 Β· updates every 60s
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