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Block #2,192,321

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/4/2017, 7:43:12 AM Β· Difficulty 10.9514 Β· 4,634,237 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
653783e4519e0f1d1e88960c737f4d520ec4a801f8c842f9ab55d3ba5b796b6e
View on Chainz β†—

Height

#2,192,321

Difficulty

10.951360

Transactions

2

Size

722 B

Version

2

Bits

0af38c51

Nonce

1,255,191,818

Timestamp

7/4/2017, 7:43:12 AM

Confirmations

4,634,237

Mined by

⛏️ P2SHAQnFXoH2cRU5LTreMwFQWtLF86xoXxsDaS

Merkle Root

5a5972327641f5f8b897d0c73c3db283d8a3a7a76a27c692618ba23e88832720
Transactions (2)
Coinbase7c9f0cb51290e8…7c13c389fbdc6c
1 in β†’ 1 out8.3400 XPM109 B
AQnFXoH2…xoXxsDaS
6a4a918f83c825…6c1d1cf4fad628
3 in β†’ 2 out1268.8407 XPM522 B
AdLv38Pf…k1z3e6DcASFZwwN9…QaFPEXj5
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.

1.310 Γ— 10⁹⁢(97-digit number)
13109031737200019447…26566138134392038401
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
1.310 Γ— 10⁹⁢(97-digit number)
13109031737200019447…26566138134392038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.621 Γ— 10⁹⁢(97-digit number)
26218063474400038895…53132276268784076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.243 Γ— 10⁹⁢(97-digit number)
52436126948800077790…06264552537568153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.048 Γ— 10⁹⁷(98-digit number)
10487225389760015558…12529105075136307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.097 Γ— 10⁹⁷(98-digit number)
20974450779520031116…25058210150272614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.194 Γ— 10⁹⁷(98-digit number)
41948901559040062232…50116420300545228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.389 Γ— 10⁹⁷(98-digit number)
83897803118080124464…00232840601090457601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.677 Γ— 10⁹⁸(99-digit number)
16779560623616024892…00465681202180915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.355 Γ— 10⁹⁸(99-digit number)
33559121247232049785…00931362404361830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.711 Γ— 10⁹⁸(99-digit number)
67118242494464099571…01862724808723660801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,856,615 XPMΒ·at block #6,826,557 Β· updates every 60s
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