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Block #2,099,736

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2017, 4:56:40 PM Β· Difficulty 10.8562 Β· 4,743,332 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
077a49139c819848d0faa8757086309a2daf40ee43d072f137973f2389e88456
View on Chainz β†—

Height

#2,099,736

Difficulty

10.856229

Transactions

1

Size

200 B

Version

2

Bits

0adb31d0

Nonce

677,086,005

Timestamp

5/4/2017, 4:56:40 PM

Confirmations

4,743,332

Mined by

⛏️ P2SHAS5g5iEbABy8Abv2n7pMkpHKo9Wb6tRmi4

Merkle Root

765d83f1e98e02d7d0292b0310d4185999aa373efd51cd537099fee4db8d24c9
Transactions (1)
Coinbase765d83f1e98e02…99fee4db8d24c9
1 in β†’ 1 out8.4700 XPM110 B
AS5g5iEb…Wb6tRmi4
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.

4.732 Γ— 10⁹⁴(95-digit number)
47328495146386613560…23334528734877863521
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
4.732 Γ— 10⁹⁴(95-digit number)
47328495146386613560…23334528734877863521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.465 Γ— 10⁹⁴(95-digit number)
94656990292773227121…46669057469755727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.893 Γ— 10⁹⁡(96-digit number)
18931398058554645424…93338114939511454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.786 Γ— 10⁹⁡(96-digit number)
37862796117109290848…86676229879022908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.572 Γ— 10⁹⁡(96-digit number)
75725592234218581697…73352459758045816321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.514 Γ— 10⁹⁢(97-digit number)
15145118446843716339…46704919516091632641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.029 Γ— 10⁹⁢(97-digit number)
30290236893687432679…93409839032183265281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.058 Γ— 10⁹⁢(97-digit number)
60580473787374865358…86819678064366530561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12116094757474973071…73639356128733061121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.423 Γ— 10⁹⁷(98-digit number)
24232189514949946143…47278712257466122241
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:57,988,902 XPMΒ·at block #6,843,067 Β· updates every 60s
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