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Block #277,356

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 1:17:44 PM Β· Difficulty 9.9660 Β· 6,523,627 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
add94fa8245a2e8d1fd65f0b3a464855871e07e3385ff9b82538cf5bc85e0629
View on Chainz β†—

Height

#277,356

Difficulty

9.965974

Transactions

1

Size

200 B

Version

2

Bits

09f74a11

Nonce

33,207

Timestamp

11/27/2013, 1:17:44 PM

Confirmations

6,523,627

Mined by

⛏️ P2SHANNQjLEpZ4WgsDvFZ5dNRmaLdVGddva1Pt

Merkle Root

b6a94eaa1e1b5ea77bdf9bc4d59f6d5a1baacf5c128263a6c3d4f269262d6039
Transactions (1)
Coinbaseb6a94eaa1e1b5e…d4f269262d6039
1 in β†’ 1 out10.0500 XPM109 B
ANNQjLEp…Gddva1Pt
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.

3.748 Γ— 10⁹⁢(97-digit number)
37488914809591913314…32202187663328706011
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
3.748 Γ— 10⁹⁢(97-digit number)
37488914809591913314…32202187663328706011
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.497 Γ— 10⁹⁢(97-digit number)
74977829619183826629…64404375326657412021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.499 Γ— 10⁹⁷(98-digit number)
14995565923836765325…28808750653314824041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.999 Γ— 10⁹⁷(98-digit number)
29991131847673530651…57617501306629648081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.998 Γ— 10⁹⁷(98-digit number)
59982263695347061303…15235002613259296161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.199 Γ— 10⁹⁸(99-digit number)
11996452739069412260…30470005226518592321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.399 Γ— 10⁹⁸(99-digit number)
23992905478138824521…60940010453037184641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.798 Γ— 10⁹⁸(99-digit number)
47985810956277649042…21880020906074369281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.597 Γ— 10⁹⁸(99-digit number)
95971621912555298085…43760041812148738561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.919 Γ— 10⁹⁹(100-digit number)
19194324382511059617…87520083624297477121
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:57,651,923 XPMΒ·at block #6,800,982 Β· updates every 60s
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