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Block #2,455,492

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/3/2018, 9:23:48 AM Β· Difficulty 10.9528 Β· 4,387,478 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
12582e6af0304ac0401c84fbf34fc98e1286e99d48f05a3961303f36f7f1c721
View on Chainz β†—

Height

#2,455,492

Difficulty

10.952820

Transactions

2

Size

1.71 KB

Version

2

Bits

0af3ec02

Nonce

631,083,521

Timestamp

1/3/2018, 9:23:48 AM

Confirmations

4,387,478

Mined by

⛏️ P2SHAZyY6gfAWKKJgoKGeVya1Y1oVb92JT9o5j

Merkle Root

eeb70355dae79bc1b0facf795e1bac2b6f63a33c558ff7cc4a89b17821364f22
Transactions (2)
Coinbasec1faa1d2dd8439…475d35a18582ef
1 in β†’ 1 out8.3400 XPM110 B
AZyY6gfA…92JT9o5j
40e32522d34ec5…8e4fea17ddd796
10 in β†’ 2 out50.0338 XPM1.52 KB
ARHY33H9…UYRL6o8LAQV2cMEF…SFfb2zE5
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.

2.549 Γ— 10⁹⁡(96-digit number)
25498628408218361212…83688455179089160639
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.549 Γ— 10⁹⁡(96-digit number)
25498628408218361212…83688455179089160639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.099 Γ— 10⁹⁡(96-digit number)
50997256816436722425…67376910358178321279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.019 Γ— 10⁹⁢(97-digit number)
10199451363287344485…34753820716356642559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.039 Γ— 10⁹⁢(97-digit number)
20398902726574688970…69507641432713285119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.079 Γ— 10⁹⁢(97-digit number)
40797805453149377940…39015282865426570239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.159 Γ— 10⁹⁢(97-digit number)
81595610906298755880…78030565730853140479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.631 Γ— 10⁹⁷(98-digit number)
16319122181259751176…56061131461706280959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.263 Γ— 10⁹⁷(98-digit number)
32638244362519502352…12122262923412561919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.527 Γ— 10⁹⁷(98-digit number)
65276488725039004704…24244525846825123839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁸(99-digit number)
13055297745007800940…48489051693650247679
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,988,112 XPMΒ·at block #6,842,969 Β· updates every 60s
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