Block #1,410,601

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/12/2016, 7:43:40 PM · Difficulty 10.8053 · 5,431,658 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ddbb763bbe56fd0949f91fa934622e3f5e04732753fcf73d2850be48b2575f78

Height

#1,410,601

Difficulty

10.805319

Transactions

2

Size

426 B

Version

2

Bits

0ace2969

Nonce

104,205,375

Timestamp

1/12/2016, 7:43:40 PM

Confirmations

5,431,658

Merkle Root

b6b0001325186c76a0fd134bb23b7172a312ee3d857eb0c03fce21991dd5134c
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.

8.694 × 10⁹⁵(96-digit number)
86942765883063866466…19713858546038581759
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
8.694 × 10⁹⁵(96-digit number)
86942765883063866466…19713858546038581759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.738 × 10⁹⁶(97-digit number)
17388553176612773293…39427717092077163519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.477 × 10⁹⁶(97-digit number)
34777106353225546586…78855434184154327039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.955 × 10⁹⁶(97-digit number)
69554212706451093172…57710868368308654079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.391 × 10⁹⁷(98-digit number)
13910842541290218634…15421736736617308159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.782 × 10⁹⁷(98-digit number)
27821685082580437269…30843473473234616319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.564 × 10⁹⁷(98-digit number)
55643370165160874538…61686946946469232639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.112 × 10⁹⁸(99-digit number)
11128674033032174907…23373893892938465279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.225 × 10⁹⁸(99-digit number)
22257348066064349815…46747787785876930559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.451 × 10⁹⁸(99-digit number)
44514696132128699630…93495575571753861119
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:57,982,470 XPM·at block #6,842,258 · updates every 60s
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