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Block #2,680,253

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/27/2018, 2:29:35 PM Β· Difficulty 11.6915 Β· 4,151,045 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b17acbb251d50b6c07112b1d241c4b38e7b1fa8e0d5e477cdf3abdb9a51c5dcf
View on Chainz β†—

Height

#2,680,253

Difficulty

11.691547

Transactions

3

Size

1.19 KB

Version

2

Bits

0bb10935

Nonce

1,176,706,317

Timestamp

5/27/2018, 2:29:35 PM

Confirmations

4,151,045

Mined by

⛏️ P2SHAUsxgf1ZHx9xdGZP82DPAdUfXD8Sk8fSG5

Merkle Root

9c79a0b882cf7d184f667050c82b43606ca8a717df488dde318fc3f6bdd8f362
Transactions (3)
Coinbase3da8dff2c49de8…9a859695532f95
1 in β†’ 1 out7.3200 XPM110 B
AUsxgf1Z…8Sk8fSG5
719d7277cd8d01…dd26d4f97e8402
1 in β†’ 2 out7.2900 XPM193 B
ATiwcg7r…Aj78zUy4AJF3RxP5…GoF8KQUr
5bb1849e3b24cb…3ef09032e1ab6b
6 in β†’ 2 out33.7416 XPM829 B
AWp4iAg7…FUBLEm8xAUfh4RwR…HTKCcb2A
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.

1.182 Γ— 10⁹⁴(95-digit number)
11823765715699400258…76962318497321644181
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
1.182 Γ— 10⁹⁴(95-digit number)
11823765715699400258…76962318497321644181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.364 Γ— 10⁹⁴(95-digit number)
23647531431398800517…53924636994643288361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.729 Γ— 10⁹⁴(95-digit number)
47295062862797601035…07849273989286576721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.459 Γ— 10⁹⁴(95-digit number)
94590125725595202070…15698547978573153441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.891 Γ— 10⁹⁡(96-digit number)
18918025145119040414…31397095957146306881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.783 Γ— 10⁹⁡(96-digit number)
37836050290238080828…62794191914292613761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.567 Γ— 10⁹⁡(96-digit number)
75672100580476161656…25588383828585227521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.513 Γ— 10⁹⁢(97-digit number)
15134420116095232331…51176767657170455041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.026 Γ— 10⁹⁢(97-digit number)
30268840232190464662…02353535314340910081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.053 Γ— 10⁹⁢(97-digit number)
60537680464380929325…04707070628681820161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.210 Γ— 10⁹⁷(98-digit number)
12107536092876185865…09414141257363640321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,894,531 XPMΒ·at block #6,831,297 Β· updates every 60s
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