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Block #1,611,055

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2016, 2:14:57 PM Β· Difficulty 10.6053 Β· 5,234,292 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09e028f7802fbcfff1151952cdbff0c9091ec0ef733d2a30d2bd73824fc13d0a
View on Chainz β†—

Height

#1,611,055

Difficulty

10.605323

Transactions

1

Size

199 B

Version

2

Bits

0a9af66f

Nonce

790,191,002

Timestamp

6/2/2016, 2:14:57 PM

Confirmations

5,234,292

Mined by

⛏️ P2SHARn26Wn6g5JzG5yaMNJbA8eHEsVN8nnGT5

Merkle Root

1106205ad4f82342547ffadce36a9cae95a7a03af3d60c488f08e9f1989261df
Transactions (1)
Coinbase1106205ad4f823…08e9f1989261df
1 in β†’ 1 out8.8800 XPM109 B
ARn26Wn6…VN8nnGT5
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.

3.526 Γ— 10⁹³(94-digit number)
35263368984761518525…38325514459886662161
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
3.526 Γ— 10⁹³(94-digit number)
35263368984761518525…38325514459886662161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.052 Γ— 10⁹³(94-digit number)
70526737969523037051…76651028919773324321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.410 Γ— 10⁹⁴(95-digit number)
14105347593904607410…53302057839546648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.821 Γ— 10⁹⁴(95-digit number)
28210695187809214820…06604115679093297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.642 Γ— 10⁹⁴(95-digit number)
56421390375618429641…13208231358186594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.128 Γ— 10⁹⁡(96-digit number)
11284278075123685928…26416462716373189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.256 Γ— 10⁹⁡(96-digit number)
22568556150247371856…52832925432746378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.513 Γ— 10⁹⁡(96-digit number)
45137112300494743713…05665850865492756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.027 Γ— 10⁹⁡(96-digit number)
90274224600989487426…11331701730985512961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.805 Γ— 10⁹⁢(97-digit number)
18054844920197897485…22663403461971025921
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:58,007,218 XPMΒ·at block #6,845,346 Β· updates every 60s
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