Block #385,218

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/1/2014, 3:32:25 PM · Difficulty 10.4048 · 6,432,055 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9f77de7adb6a6a713f06df64733dd1365e01710e574b079a411cb7d800e0155e

Height

#385,218

Difficulty

10.404793

Transactions

2

Size

361 B

Version

2

Bits

0a67a087

Nonce

2,639

Timestamp

2/1/2014, 3:32:25 PM

Confirmations

6,432,055

Merkle Root

0707f08818ff01b405130e37aa665a5952cb2e955932875498320cfd70a0dde3
Transactions (2)
1 in → 1 out9.2300 XPM110 B
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.345 × 10¹⁰¹(102-digit number)
13456066178972300798…67560880608701948959
Discovered Prime Numbers
p_k = 2^k × 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
1.345 × 10¹⁰¹(102-digit number)
13456066178972300798…67560880608701948959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.691 × 10¹⁰¹(102-digit number)
26912132357944601597…35121761217403897919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.382 × 10¹⁰¹(102-digit number)
53824264715889203195…70243522434807795839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.076 × 10¹⁰²(103-digit number)
10764852943177840639…40487044869615591679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.152 × 10¹⁰²(103-digit number)
21529705886355681278…80974089739231183359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.305 × 10¹⁰²(103-digit number)
43059411772711362556…61948179478462366719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.611 × 10¹⁰²(103-digit number)
86118823545422725112…23896358956924733439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.722 × 10¹⁰³(104-digit number)
17223764709084545022…47792717913849466879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.444 × 10¹⁰³(104-digit number)
34447529418169090045…95585435827698933759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.889 × 10¹⁰³(104-digit number)
68895058836338180090…91170871655397867519
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,782,222 XPM·at block #6,817,272 · updates every 60s
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