Block #1,205,426

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/23/2015, 11:26:25 AM · Difficulty 10.7895 · 5,636,063 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
45a6bcaa1c95821fc745dbb23730784b89a8e7de54be93b0fe7cddc94dbb5528

Height

#1,205,426

Difficulty

10.789451

Transactions

2

Size

1016 B

Version

2

Bits

0aca197e

Nonce

936,472,794

Timestamp

8/23/2015, 11:26:25 AM

Confirmations

5,636,063

Merkle Root

95dc615b6f88861f1106153450721a4368d57be139cea33c094eb47bafd55f55
Transactions (2)
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.

4.366 × 10⁹⁴(95-digit number)
43667715524953523253…17163372253294445959
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
4.366 × 10⁹⁴(95-digit number)
43667715524953523253…17163372253294445959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.733 × 10⁹⁴(95-digit number)
87335431049907046507…34326744506588891919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.746 × 10⁹⁵(96-digit number)
17467086209981409301…68653489013177783839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.493 × 10⁹⁵(96-digit number)
34934172419962818603…37306978026355567679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.986 × 10⁹⁵(96-digit number)
69868344839925637206…74613956052711135359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.397 × 10⁹⁶(97-digit number)
13973668967985127441…49227912105422270719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.794 × 10⁹⁶(97-digit number)
27947337935970254882…98455824210844541439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.589 × 10⁹⁶(97-digit number)
55894675871940509764…96911648421689082879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.117 × 10⁹⁷(98-digit number)
11178935174388101952…93823296843378165759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.235 × 10⁹⁷(98-digit number)
22357870348776203905…87646593686756331519
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:57,976,288 XPM·at block #6,841,488 · updates every 60s
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