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Block #1,894,920

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/15/2016, 7:04:00 AM Β· Difficulty 10.7477 Β· 4,931,194 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
161ec849d1df805cb66da8c6793d8c4e8b7238c024607f15534ff680d175094b
View on Chainz β†—

Height

#1,894,920

Difficulty

10.747655

Transactions

1

Size

201 B

Version

2

Bits

0abf6650

Nonce

799,944,515

Timestamp

12/15/2016, 7:04:00 AM

Confirmations

4,931,194

Mined by

⛏️ P2SHAHLZ9Dx8tZuRjMPfGSMffkayskQ8tPcPF1

Merkle Root

8fe19401ff8ebfec01e5561e19b380d4a7f11d1ac8a0a51848f0f77a27fd2025
Transactions (1)
Coinbase8fe19401ff8ebf…f0f77a27fd2025
1 in β†’ 1 out8.6400 XPM110 B
AHLZ9Dx8…Q8tPcPF1
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.

1.263 Γ— 10⁹⁷(98-digit number)
12631293857657727041…56683402018257182721
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
1.263 Γ— 10⁹⁷(98-digit number)
12631293857657727041…56683402018257182721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.526 Γ— 10⁹⁷(98-digit number)
25262587715315454083…13366804036514365441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.052 Γ— 10⁹⁷(98-digit number)
50525175430630908166…26733608073028730881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.010 Γ— 10⁹⁸(99-digit number)
10105035086126181633…53467216146057461761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.021 Γ— 10⁹⁸(99-digit number)
20210070172252363266…06934432292114923521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.042 Γ— 10⁹⁸(99-digit number)
40420140344504726532…13868864584229847041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.084 Γ— 10⁹⁸(99-digit number)
80840280689009453065…27737729168459694081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.616 Γ— 10⁹⁹(100-digit number)
16168056137801890613…55475458336919388161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.233 Γ— 10⁹⁹(100-digit number)
32336112275603781226…10950916673838776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.467 Γ— 10⁹⁹(100-digit number)
64672224551207562452…21901833347677552641
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:57,853,037 XPMΒ·at block #6,826,113 Β· updates every 60s
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