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Block #2,653,759

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/8/2018, 4:38:51 PM Β· Difficulty 11.7327 Β· 4,177,117 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b62f48537c27a62ae85741f9c2806e286f88203f0696da3781e9167740fcdbc3
View on Chainz β†—

Height

#2,653,759

Difficulty

11.732658

Transactions

1

Size

201 B

Version

2

Bits

0bbb8f73

Nonce

361,772,412

Timestamp

5/8/2018, 4:38:51 PM

Confirmations

4,177,117

Mined by

⛏️ P2SHAYd3Pfqqxf7KZmNXjiucK42UEwJp4qtt1F

Merkle Root

9f82130a2c75670e72f24d3de291517ee9a298f87d22a408f92ec15886902854
Transactions (1)
Coinbase9f82130a2c7567…2ec15886902854
1 in β†’ 1 out7.2500 XPM110 B
AYd3Pfqq…Jp4qtt1F
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.

1.269 Γ— 10⁹⁷(98-digit number)
12690866542429837861…65525331070489518079
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
1.269 Γ— 10⁹⁷(98-digit number)
12690866542429837861…65525331070489518079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.538 Γ— 10⁹⁷(98-digit number)
25381733084859675723…31050662140979036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.076 Γ— 10⁹⁷(98-digit number)
50763466169719351447…62101324281958072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁸(99-digit number)
10152693233943870289…24202648563916144639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.030 Γ— 10⁹⁸(99-digit number)
20305386467887740579…48405297127832289279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.061 Γ— 10⁹⁸(99-digit number)
40610772935775481158…96810594255664578559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.122 Γ— 10⁹⁸(99-digit number)
81221545871550962316…93621188511329157119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.624 Γ— 10⁹⁹(100-digit number)
16244309174310192463…87242377022658314239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.248 Γ— 10⁹⁹(100-digit number)
32488618348620384926…74484754045316628479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.497 Γ— 10⁹⁹(100-digit number)
64977236697240769852…48969508090633256959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.299 Γ— 10¹⁰⁰(101-digit number)
12995447339448153970…97939016181266513919
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,891,146 XPMΒ·at block #6,830,875 Β· updates every 60s
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