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Block #2,721,663

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/26/2018, 3:20:30 AM Β· Difficulty 11.6163 Β· 4,119,842 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
557a82746789550699b67d3027532d32fb88b69a86bd25edf9c2c08cf628ea2d
View on Chainz β†—

Height

#2,721,663

Difficulty

11.616259

Transactions

2

Size

871 B

Version

2

Bits

0b9dc320

Nonce

721,502,834

Timestamp

6/26/2018, 3:20:30 AM

Confirmations

4,119,842

Mined by

⛏️ P2SHAXvRR3Uz7nmMcXpY1SDcK3GUUg4iPAkuJX

Merkle Root

7e23585e7732bf9556e2abd90669e4ce419b7391264b5915a9042d82d3d453b1
Transactions (2)
Coinbaseefeaa21bf295e2…e2c0809768916a
1 in β†’ 1 out7.4100 XPM110 B
AXvRR3Uz…4iPAkuJX
c62426af524eb9…cc6ffbee53eb01
4 in β†’ 2 out19.4241 XPM671 B
AdNMj778…oUbrbuCSAahYoALp…A9oMoEQY
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.

9.163 Γ— 10⁹³(94-digit number)
91636192438807094688…45509535225497817519
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
9.163 Γ— 10⁹³(94-digit number)
91636192438807094688…45509535225497817519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.832 Γ— 10⁹⁴(95-digit number)
18327238487761418937…91019070450995635039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.665 Γ— 10⁹⁴(95-digit number)
36654476975522837875…82038140901991270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.330 Γ— 10⁹⁴(95-digit number)
73308953951045675750…64076281803982540159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.466 Γ— 10⁹⁡(96-digit number)
14661790790209135150…28152563607965080319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.932 Γ— 10⁹⁡(96-digit number)
29323581580418270300…56305127215930160639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.864 Γ— 10⁹⁡(96-digit number)
58647163160836540600…12610254431860321279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.172 Γ— 10⁹⁢(97-digit number)
11729432632167308120…25220508863720642559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.345 Γ— 10⁹⁢(97-digit number)
23458865264334616240…50441017727441285119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.691 Γ— 10⁹⁢(97-digit number)
46917730528669232480…00882035454882570239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.383 Γ— 10⁹⁢(97-digit number)
93835461057338464961…01764070909765140479
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:57,976,419 XPMΒ·at block #6,841,504 Β· updates every 60s
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