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Block #2,096,737

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2017, 5:09:00 AM Β· Difficulty 10.8720 Β· 4,739,778 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fe64bdbb0e8d7369e50c9210d8cedc93b8dbc12c94b6b3a222b3a650fdb8cd1b
View on Chainz β†—

Height

#2,096,737

Difficulty

10.872018

Transactions

1

Size

208 B

Version

2

Bits

0adf3c8d

Nonce

381,613,492

Timestamp

5/2/2017, 5:09:00 AM

Confirmations

4,739,778

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

6dd392a12fe9630b100f1aa8210ec74e7780b722152a483b357d33110a035298
Transactions (1)
Coinbase6dd392a12fe963…7d33110a035298
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.

3.431 Γ— 10⁹⁡(96-digit number)
34313978823815353126…58865953307443567681
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
3.431 Γ— 10⁹⁡(96-digit number)
34313978823815353126…58865953307443567681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.862 Γ— 10⁹⁡(96-digit number)
68627957647630706252…17731906614887135361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.372 Γ— 10⁹⁢(97-digit number)
13725591529526141250…35463813229774270721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.745 Γ— 10⁹⁢(97-digit number)
27451183059052282500…70927626459548541441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.490 Γ— 10⁹⁢(97-digit number)
54902366118104565001…41855252919097082881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.098 Γ— 10⁹⁷(98-digit number)
10980473223620913000…83710505838194165761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.196 Γ— 10⁹⁷(98-digit number)
21960946447241826000…67421011676388331521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.392 Γ— 10⁹⁷(98-digit number)
43921892894483652001…34842023352776663041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.784 Γ— 10⁹⁷(98-digit number)
87843785788967304002…69684046705553326081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.756 Γ— 10⁹⁸(99-digit number)
17568757157793460800…39368093411106652161
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:57,936,396 XPMΒ·at block #6,836,514 Β· updates every 60s
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