Block #389,256

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2014, 9:17:03 AM · Difficulty 10.4175 · 6,435,594 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37efe40c2e304d3a654635710bc3e0ac473736882170f105539bb6cc84f96df6

Height

#389,256

Difficulty

10.417464

Transactions

1

Size

767 B

Version

2

Bits

0a6adeea

Nonce

466,100

Timestamp

2/4/2014, 9:17:03 AM

Confirmations

6,435,594

Merkle Root

d9b82ca6c336df7f030d2aa58f64db4b1baa9384a268422af8775d3c9a7d0e3d
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.

4.980 × 10¹⁰⁰(101-digit number)
49801681090774866911…79440081905373886799
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
4.980 × 10¹⁰⁰(101-digit number)
49801681090774866911…79440081905373886799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.960 × 10¹⁰⁰(101-digit number)
99603362181549733823…58880163810747773599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.992 × 10¹⁰¹(102-digit number)
19920672436309946764…17760327621495547199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.984 × 10¹⁰¹(102-digit number)
39841344872619893529…35520655242991094399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.968 × 10¹⁰¹(102-digit number)
79682689745239787059…71041310485982188799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.593 × 10¹⁰²(103-digit number)
15936537949047957411…42082620971964377599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.187 × 10¹⁰²(103-digit number)
31873075898095914823…84165241943928755199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.374 × 10¹⁰²(103-digit number)
63746151796191829647…68330483887857510399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.274 × 10¹⁰³(104-digit number)
12749230359238365929…36660967775715020799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.549 × 10¹⁰³(104-digit number)
25498460718476731858…73321935551430041599
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:57,842,882 XPM·at block #6,824,849 · updates every 60s
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