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Block #2,096,288

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2017, 9:43:54 PM Β· Difficulty 10.8719 Β· 4,736,738 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dd9b8354fb889774e5bf8196694ccf6a45c0c7d1a39600163ba4070a8813b56a
View on Chainz β†—

Height

#2,096,288

Difficulty

10.871888

Transactions

1

Size

209 B

Version

2

Bits

0adf3414

Nonce

217,833,172

Timestamp

5/1/2017, 9:43:54 PM

Confirmations

4,736,738

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

7f045923d1a8be343f63310c5a77d5a43d34e3de238e9a80f165d25df71bfb2c
Transactions (1)
Coinbase7f045923d1a8be…65d25df71bfb2c
1 in β†’ 1 out8.4500 XPM118 B
AM6GYpjw…aw86QDtR
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.

7.608 Γ— 10⁹⁢(97-digit number)
76081334130074384874…75125775839750881279
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.608 Γ— 10⁹⁢(97-digit number)
76081334130074384874…75125775839750881279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.521 Γ— 10⁹⁷(98-digit number)
15216266826014876974…50251551679501762559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.043 Γ— 10⁹⁷(98-digit number)
30432533652029753949…00503103359003525119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.086 Γ— 10⁹⁷(98-digit number)
60865067304059507899…01006206718007050239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁸(99-digit number)
12173013460811901579…02012413436014100479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.434 Γ— 10⁹⁸(99-digit number)
24346026921623803159…04024826872028200959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.869 Γ— 10⁹⁸(99-digit number)
48692053843247606319…08049653744056401919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.738 Γ— 10⁹⁸(99-digit number)
97384107686495212639…16099307488112803839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁹(100-digit number)
19476821537299042527…32198614976225607679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.895 Γ— 10⁹⁹(100-digit number)
38953643074598085055…64397229952451215359
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,908,384 XPMΒ·at block #6,833,025 Β· updates every 60s
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