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Block #2,924,823

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2018, 2:24:46 AM Β· Difficulty 11.3572 Β· 3,919,024 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2deba732259ce3192acdf4830f504d2e39d299fc40c924f2a48a02805f8074d4
View on Chainz β†—

Height

#2,924,823

Difficulty

11.357185

Transactions

1

Size

201 B

Version

2

Bits

0b5b707b

Nonce

514,645,964

Timestamp

11/16/2018, 2:24:46 AM

Confirmations

3,919,024

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

2faecfc9c9ec24fb2bbe65a9f38c481cf12db531ef5b4060918beb68ceb4c72b
Transactions (1)
Coinbase2faecfc9c9ec24…8beb68ceb4c72b
1 in β†’ 1 out7.7400 XPM110 B
AUhjokok…k5m93PZR
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.

1.004 Γ— 10⁹⁷(98-digit number)
10042405798068551210…26271342959525416961
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
1.004 Γ— 10⁹⁷(98-digit number)
10042405798068551210…26271342959525416961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.008 Γ— 10⁹⁷(98-digit number)
20084811596137102421…52542685919050833921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.016 Γ— 10⁹⁷(98-digit number)
40169623192274204842…05085371838101667841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.033 Γ— 10⁹⁷(98-digit number)
80339246384548409684…10170743676203335681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.606 Γ— 10⁹⁸(99-digit number)
16067849276909681936…20341487352406671361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.213 Γ— 10⁹⁸(99-digit number)
32135698553819363873…40682974704813342721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.427 Γ— 10⁹⁸(99-digit number)
64271397107638727747…81365949409626685441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.285 Γ— 10⁹⁹(100-digit number)
12854279421527745549…62731898819253370881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.570 Γ— 10⁹⁹(100-digit number)
25708558843055491099…25463797638506741761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.141 Γ— 10⁹⁹(100-digit number)
51417117686110982198…50927595277013483521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.028 Γ— 10¹⁰⁰(101-digit number)
10283423537222196439…01855190554026967041
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:57,995,142 XPMΒ·at block #6,843,846 Β· updates every 60s
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