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Block #3,255,121

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/5/2019, 11:55:46 PM Β· Difficulty 10.9960 Β· 3,587,735 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6e193caecb2e5aabbda6fa03154d89b7a5a222b221bab8b42d4e5462abcd881f
View on Chainz β†—

Height

#3,255,121

Difficulty

10.996023

Transactions

2

Size

6.94 KB

Version

2

Bits

0afefb5f

Nonce

320,030,523

Timestamp

7/5/2019, 11:55:46 PM

Confirmations

3,587,735

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

2d2a73e00c2e146062fbbe00c43051dc41dfdd6ef07b9021c0e19faf04d84112
Transactions (2)
Coinbase759c5d9b378d57…2ac9c10a1bcb90
1 in β†’ 1 out8.3300 XPM110 B
ASiq2qtK…VMhmk7yL
c97dcb74d81ddd…3035cb02ff18b4
60 in β†’ 2 out496.3200 XPM6.74 KB
AFybbP2J…hk38SED1AeEUjeK4…nYAVnjdo
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.

1.100 Γ— 10⁹⁴(95-digit number)
11006650357439112196…60491373919233524161
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
1.100 Γ— 10⁹⁴(95-digit number)
11006650357439112196…60491373919233524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.201 Γ— 10⁹⁴(95-digit number)
22013300714878224393…20982747838467048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.402 Γ— 10⁹⁴(95-digit number)
44026601429756448786…41965495676934096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.805 Γ— 10⁹⁴(95-digit number)
88053202859512897572…83930991353868193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.761 Γ— 10⁹⁡(96-digit number)
17610640571902579514…67861982707736386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.522 Γ— 10⁹⁡(96-digit number)
35221281143805159028…35723965415472773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.044 Γ— 10⁹⁡(96-digit number)
70442562287610318057…71447930830945546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.408 Γ— 10⁹⁢(97-digit number)
14088512457522063611…42895861661891092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.817 Γ— 10⁹⁢(97-digit number)
28177024915044127223…85791723323782184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.635 Γ— 10⁹⁢(97-digit number)
56354049830088254446…71583446647564369921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.127 Γ— 10⁹⁷(98-digit number)
11270809966017650889…43166893295128739841
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:57,987,195 XPMΒ·at block #6,842,855 Β· updates every 60s
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