Block #801,079

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/7/2014, 9:08:09 AM · Difficulty 10.9762 · 6,015,513 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b3dd9512bc31aae7c8fbccde83bf8d2b5edbd0d65d8dfd66ab97df268a19b1f9

Height

#801,079

Difficulty

10.976174

Transactions

5

Size

1.52 KB

Version

2

Bits

0af9e68e

Nonce

1,085,947,880

Timestamp

11/7/2014, 9:08:09 AM

Confirmations

6,015,513

Merkle Root

a7a866193c7d4e24d01f60d3a33d5a8857a766ff1d7592a6a4cc0827f0e81d53
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.

3.998 × 10⁹⁷(98-digit number)
39984059148873188380…27342992872016650239
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
3.998 × 10⁹⁷(98-digit number)
39984059148873188380…27342992872016650239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.996 × 10⁹⁷(98-digit number)
79968118297746376760…54685985744033300479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.599 × 10⁹⁸(99-digit number)
15993623659549275352…09371971488066600959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.198 × 10⁹⁸(99-digit number)
31987247319098550704…18743942976133201919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.397 × 10⁹⁸(99-digit number)
63974494638197101408…37487885952266403839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.279 × 10⁹⁹(100-digit number)
12794898927639420281…74975771904532807679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.558 × 10⁹⁹(100-digit number)
25589797855278840563…49951543809065615359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.117 × 10⁹⁹(100-digit number)
51179595710557681126…99903087618131230719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.023 × 10¹⁰⁰(101-digit number)
10235919142111536225…99806175236262461439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.047 × 10¹⁰⁰(101-digit number)
20471838284223072450…99612350472524922879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.094 × 10¹⁰⁰(101-digit number)
40943676568446144901…99224700945049845759
Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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
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 × 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:57,776,860 XPM·at block #6,816,591 · updates every 60s
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