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Block #1,735,518

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2016, 8:50:32 PM Β· Difficulty 10.7209 Β· 5,109,312 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
068e1ecb6c48c4aadeb20d7567016b3efb53663f9d4e93e8894ac462886b328b
View on Chainz β†—

Height

#1,735,518

Difficulty

10.720892

Transactions

1

Size

243 B

Version

2

Bits

0ab88c69

Nonce

2,014,073

Timestamp

8/26/2016, 8:50:32 PM

Confirmations

5,109,312

Mined by

⛏️ P2SHAGkY5Euz5mzpuyGoaReCtspzag5TxsxHeG

Merkle Root

409129d9eab9ec423b55d53fcf07d1d94ea871303e771e68134596d60a0bab23
Transactions (1)
Coinbase409129d9eab9ec…4596d60a0bab23
1 in β†’ 2 out8.6900 XPM152 B
AGkY5Euz…5TxsxHeGALPu3s2c…EJXLjVFh
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.

1.634 Γ— 10⁹⁸(99-digit number)
16349722881145193383…18444934125434060801
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
1.634 Γ— 10⁹⁸(99-digit number)
16349722881145193383…18444934125434060801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.269 Γ— 10⁹⁸(99-digit number)
32699445762290386767…36889868250868121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.539 Γ— 10⁹⁸(99-digit number)
65398891524580773535…73779736501736243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.307 Γ— 10⁹⁹(100-digit number)
13079778304916154707…47559473003472486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.615 Γ— 10⁹⁹(100-digit number)
26159556609832309414…95118946006944972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.231 Γ— 10⁹⁹(100-digit number)
52319113219664618828…90237892013889945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.046 Γ— 10¹⁰⁰(101-digit number)
10463822643932923765…80475784027779891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.092 Γ— 10¹⁰⁰(101-digit number)
20927645287865847531…60951568055559782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.185 Γ— 10¹⁰⁰(101-digit number)
41855290575731695062…21903136111119564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.371 Γ— 10¹⁰⁰(101-digit number)
83710581151463390125…43806272222239129601
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:58,003,049 XPMΒ·at block #6,844,829 Β· updates every 60s
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