Block #1,260,509

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/30/2015, 5:10:30 AM · Difficulty 10.8196 · 5,547,611 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
79cc4c7b40bbe4834efc351d3c7a301a18eb7406af0f2fba9ac894b87e3b88ac

Height

#1,260,509

Difficulty

10.819646

Transactions

4

Size

878 B

Version

2

Bits

0ad1d44e

Nonce

100,001,867

Timestamp

9/30/2015, 5:10:30 AM

Confirmations

5,547,611

Merkle Root

992e67b9e6197d6e2db081531cfa3d15f90a172d77f7496d3e3fd530f78e03ad
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.

7.519 × 10⁹⁴(95-digit number)
75194616142416608570…56501788965153020399
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
7.519 × 10⁹⁴(95-digit number)
75194616142416608570…56501788965153020399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.503 × 10⁹⁵(96-digit number)
15038923228483321714…13003577930306040799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.007 × 10⁹⁵(96-digit number)
30077846456966643428…26007155860612081599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.015 × 10⁹⁵(96-digit number)
60155692913933286856…52014311721224163199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.203 × 10⁹⁶(97-digit number)
12031138582786657371…04028623442448326399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.406 × 10⁹⁶(97-digit number)
24062277165573314742…08057246884896652799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.812 × 10⁹⁶(97-digit number)
48124554331146629484…16114493769793305599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.624 × 10⁹⁶(97-digit number)
96249108662293258969…32228987539586611199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.924 × 10⁹⁷(98-digit number)
19249821732458651793…64457975079173222399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.849 × 10⁹⁷(98-digit number)
38499643464917303587…28915950158346444799
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:57,708,999 XPM·at block #6,808,119 · updates every 60s
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