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Block #2,833,289

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 3:42:19 PM Β· Difficulty 11.7152 Β· 4,009,023 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a29e08823e77905c4de3432b590ee8a7dcbd4d39a00703366a6c8c168cd4d465
View on Chainz β†—

Height

#2,833,289

Difficulty

11.715206

Transactions

1

Size

199 B

Version

2

Bits

0bb717c0

Nonce

1,194,654,780

Timestamp

9/10/2018, 3:42:19 PM

Confirmations

4,009,023

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

e61d7ab782b8d341fe3d73f91277485bb72714c5aaa5784798154fed26aee4a6
Transactions (1)
Coinbasee61d7ab782b8d3…154fed26aee4a6
1 in β†’ 1 out7.2700 XPM110 B
AZtxQr2F…7grUWrUz
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.

3.665 Γ— 10⁹¹(92-digit number)
36653026477918112860…69214975712610729281
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
3.665 Γ— 10⁹¹(92-digit number)
36653026477918112860…69214975712610729281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.330 Γ— 10⁹¹(92-digit number)
73306052955836225720…38429951425221458561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.466 Γ— 10⁹²(93-digit number)
14661210591167245144…76859902850442917121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.932 Γ— 10⁹²(93-digit number)
29322421182334490288…53719805700885834241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.864 Γ— 10⁹²(93-digit number)
58644842364668980576…07439611401771668481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.172 Γ— 10⁹³(94-digit number)
11728968472933796115…14879222803543336961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.345 Γ— 10⁹³(94-digit number)
23457936945867592230…29758445607086673921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.691 Γ— 10⁹³(94-digit number)
46915873891735184460…59516891214173347841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.383 Γ— 10⁹³(94-digit number)
93831747783470368921…19033782428346695681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.876 Γ— 10⁹⁴(95-digit number)
18766349556694073784…38067564856693391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.753 Γ— 10⁹⁴(95-digit number)
37532699113388147568…76135129713386782721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
7.506 Γ— 10⁹⁴(95-digit number)
75065398226776295137…52270259426773565441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,982,903 XPMΒ·at block #6,842,311 Β· updates every 60s
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