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Block #3,087,342

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/10/2019, 8:25:44 PM Β· Difficulty 11.0381 Β· 3,754,635 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
48b807b79eadec057303f86ec7e47ee9cd80f6793611b9a3cec135eaa144d8a1
View on Chainz β†—

Height

#3,087,342

Difficulty

11.038127

Transactions

1

Size

201 B

Version

2

Bits

0b09c2b3

Nonce

945,535,724

Timestamp

3/10/2019, 8:25:44 PM

Confirmations

3,754,635

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

2a954147a1a40d44613d005045d97e4bf436f006655228d2cfa5227a82fa5812
Transactions (1)
Coinbase2a954147a1a40d…a5227a82fa5812
1 in β†’ 1 out8.1900 XPM110 B
AUhjokok…k5m93PZR
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.

1.632 Γ— 10⁹⁢(97-digit number)
16326424889846133019…20196125988270888961
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
1.632 Γ— 10⁹⁢(97-digit number)
16326424889846133019…20196125988270888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.265 Γ— 10⁹⁢(97-digit number)
32652849779692266039…40392251976541777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.530 Γ— 10⁹⁢(97-digit number)
65305699559384532079…80784503953083555841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.306 Γ— 10⁹⁷(98-digit number)
13061139911876906415…61569007906167111681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.612 Γ— 10⁹⁷(98-digit number)
26122279823753812831…23138015812334223361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.224 Γ— 10⁹⁷(98-digit number)
52244559647507625663…46276031624668446721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.044 Γ— 10⁹⁸(99-digit number)
10448911929501525132…92552063249336893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.089 Γ— 10⁹⁸(99-digit number)
20897823859003050265…85104126498673786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.179 Γ— 10⁹⁸(99-digit number)
41795647718006100531…70208252997347573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.359 Γ— 10⁹⁸(99-digit number)
83591295436012201062…40416505994695147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.671 Γ— 10⁹⁹(100-digit number)
16718259087202440212…80833011989390295041
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:57,980,201 XPMΒ·at block #6,841,976 Β· updates every 60s
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