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Block #3,085,465

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/9/2019, 1:49:22 PM Β· Difficulty 11.0311 Β· 3,751,521 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bca192b1fe17f5c2f0a6a0516b90a27ccfcbd168d8be4079434f370727b3a76
View on Chainz β†—

Height

#3,085,465

Difficulty

11.031095

Transactions

2

Size

722 B

Version

2

Bits

0b07f5d0

Nonce

726,887,252

Timestamp

3/9/2019, 1:49:22 PM

Confirmations

3,751,521

Mined by

⛏️ uAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

4c598c1546264e28c74b80fedebe8634f905f51148fb26dbbbd72f82740b7bd8
Transactions (2)
Coinbased3a79d4a03b2ef…186f5f0c68b93e
1 in β†’ 1 out8.2100 XPM109 B
AUMQRepm…tAfKmdW1
38d74cf3ee6e29…4b0b5b5d7ed517
3 in β†’ 2 out8680.4976 XPM523 B
AVZM1FPo…Y1zyWpN4AeTHTL7A…vT1872bk
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.

7.125 Γ— 10⁹⁴(95-digit number)
71253685682559633621…43168924630923867841
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
7.125 Γ— 10⁹⁴(95-digit number)
71253685682559633621…43168924630923867841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.425 Γ— 10⁹⁡(96-digit number)
14250737136511926724…86337849261847735681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.850 Γ— 10⁹⁡(96-digit number)
28501474273023853448…72675698523695471361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.700 Γ— 10⁹⁡(96-digit number)
57002948546047706896…45351397047390942721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.140 Γ— 10⁹⁢(97-digit number)
11400589709209541379…90702794094781885441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.280 Γ— 10⁹⁢(97-digit number)
22801179418419082758…81405588189563770881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.560 Γ— 10⁹⁢(97-digit number)
45602358836838165517…62811176379127541761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.120 Γ— 10⁹⁢(97-digit number)
91204717673676331034…25622352758255083521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.824 Γ— 10⁹⁷(98-digit number)
18240943534735266206…51244705516510167041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.648 Γ— 10⁹⁷(98-digit number)
36481887069470532413…02489411033020334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.296 Γ— 10⁹⁷(98-digit number)
72963774138941064827…04978822066040668161
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:57,940,188 XPMΒ·at block #6,836,985 Β· updates every 60s
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