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Block #2,103,698

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2017, 10:33:26 PM Β· Difficulty 10.8761 Β· 4,729,281 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c60e635a1f7cf2253b5262177e2441ff0c6ff36bcd0bdeb76bb6601cf08d681
View on Chainz β†—

Height

#2,103,698

Difficulty

10.876138

Transactions

2

Size

425 B

Version

2

Bits

0ae04a94

Nonce

1,533,502,901

Timestamp

5/6/2017, 10:33:26 PM

Confirmations

4,729,281

Mined by

⛏️ P2SHAWCbeh3GrjLzAEaHViPyuXdZPhWuMV2hAb

Merkle Root

137efb3b3b5e8117f0f8fe3e16f01e4d4bf9d71920bfbb9196c07b8b91212311
Transactions (2)
Coinbaseaaffa485b28926…5d9ee7362be466
1 in β†’ 1 out8.4500 XPM110 B
AWCbeh3G…WuMV2hAb
d251a8b01c0431…e04d8fe169fc20
1 in β†’ 2 out4.1362 XPM225 B
AWVjKLvH…7nBExMk3ANfYmR5g…nB9aX4Tp
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.

1.978 Γ— 10⁹⁴(95-digit number)
19787345715509509182…35263806131458251521
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
1.978 Γ— 10⁹⁴(95-digit number)
19787345715509509182…35263806131458251521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.957 Γ— 10⁹⁴(95-digit number)
39574691431019018365…70527612262916503041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.914 Γ— 10⁹⁴(95-digit number)
79149382862038036731…41055224525833006081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.582 Γ— 10⁹⁡(96-digit number)
15829876572407607346…82110449051666012161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.165 Γ— 10⁹⁡(96-digit number)
31659753144815214692…64220898103332024321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.331 Γ— 10⁹⁡(96-digit number)
63319506289630429385…28441796206664048641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.266 Γ— 10⁹⁢(97-digit number)
12663901257926085877…56883592413328097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.532 Γ— 10⁹⁢(97-digit number)
25327802515852171754…13767184826656194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.065 Γ— 10⁹⁢(97-digit number)
50655605031704343508…27534369653312389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.013 Γ— 10⁹⁷(98-digit number)
10131121006340868701…55068739306624778241
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:57,908,011 XPMΒ·at block #6,832,978 Β· updates every 60s
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