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Block #2,104,749

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/7/2017, 12:58:21 PM Β· Difficulty 10.8806 Β· 4,703,060 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fec2c9fac415dbf25f2fee609279b2dc7485ef2537838215a76bb631ab395653
View on Chainz β†—

Height

#2,104,749

Difficulty

10.880642

Transactions

2

Size

2.26 KB

Version

2

Bits

0ae171c1

Nonce

644,343,570

Timestamp

5/7/2017, 12:58:21 PM

Confirmations

4,703,060

Mined by

⛏️ P2SHAQQ3NgcKZbkELD1KUtZEtpajZ1p55Ljr3X

Merkle Root

cd42a75a98568b40e2e1fa3e05053ad897248dc2ec7e8828a4ff54fa3addc505
Transactions (2)
Coinbasecbfedf48c02b01…79a24a3cc6613d
1 in β†’ 1 out8.4600 XPM109 B
AQQ3NgcK…p55Ljr3X
31180eee5bb0ff…17b88a74430857
14 in β†’ 1 out23.8926 XPM2.07 KB
AWSXrMTW…qa1KtWPQ
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.

2.331 Γ— 10⁹³(94-digit number)
23317759180029968902…63674679068536632251
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
2.331 Γ— 10⁹³(94-digit number)
23317759180029968902…63674679068536632251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.663 Γ— 10⁹³(94-digit number)
46635518360059937805…27349358137073264501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.327 Γ— 10⁹³(94-digit number)
93271036720119875611…54698716274146529001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.865 Γ— 10⁹⁴(95-digit number)
18654207344023975122…09397432548293058001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.730 Γ— 10⁹⁴(95-digit number)
37308414688047950244…18794865096586116001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.461 Γ— 10⁹⁴(95-digit number)
74616829376095900489…37589730193172232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.492 Γ— 10⁹⁡(96-digit number)
14923365875219180097…75179460386344464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.984 Γ— 10⁹⁡(96-digit number)
29846731750438360195…50358920772688928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.969 Γ— 10⁹⁡(96-digit number)
59693463500876720391…00717841545377856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.193 Γ— 10⁹⁢(97-digit number)
11938692700175344078…01435683090755712001
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:57,706,507 XPMΒ·at block #6,807,808 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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