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Block #2,792,125

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2018, 12:11:28 PM Β· Difficulty 11.6756 Β· 4,041,514 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f86e1c781e15a855e33fc4cb6175973330e769931b19ed8958ded21d36a69b4f
View on Chainz β†—

Height

#2,792,125

Difficulty

11.675620

Transactions

2

Size

1.14 KB

Version

2

Bits

0bacf56b

Nonce

2,000,479,913

Timestamp

8/13/2018, 12:11:28 PM

Confirmations

4,041,514

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

a452a55feee01c866ceb8a4d57d26e2560b1c2ebaa46d43ea7ff22f225de1443
Transactions (2)
Coinbaseca3026941ca6f2…3b353aa46a29ee
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
ef8b33590b4660…96c08ba5413305
6 in β†’ 2 out3252.7665 XPM964 B
AMRycWoF…13hkF5ouAe4dWcPM…H2az6jGU
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.

7.017 Γ— 10⁹⁡(96-digit number)
70176584605476382685…90020309600822855681
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
7.017 Γ— 10⁹⁡(96-digit number)
70176584605476382685…90020309600822855681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.403 Γ— 10⁹⁢(97-digit number)
14035316921095276537…80040619201645711361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.807 Γ— 10⁹⁢(97-digit number)
28070633842190553074…60081238403291422721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.614 Γ— 10⁹⁢(97-digit number)
56141267684381106148…20162476806582845441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.122 Γ— 10⁹⁷(98-digit number)
11228253536876221229…40324953613165690881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.245 Γ— 10⁹⁷(98-digit number)
22456507073752442459…80649907226331381761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.491 Γ— 10⁹⁷(98-digit number)
44913014147504884918…61299814452662763521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.982 Γ— 10⁹⁷(98-digit number)
89826028295009769837…22599628905325527041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.796 Γ— 10⁹⁸(99-digit number)
17965205659001953967…45199257810651054081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.593 Γ— 10⁹⁸(99-digit number)
35930411318003907934…90398515621302108161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.186 Γ— 10⁹⁸(99-digit number)
71860822636007815869…80797031242604216321
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:57,913,324 XPMΒ·at block #6,833,638 Β· updates every 60s
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