Block #1,105,486

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/15/2015, 12:51:19 AM · Difficulty 10.7832 · 5,706,920 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ac94343b2b587c45fc84feb4fe6b96e9e486e7c2d9649f60f39287e9e5bce03

Height

#1,105,486

Difficulty

10.783213

Transactions

2

Size

2.73 KB

Version

2

Bits

0ac880ae

Nonce

644,041,083

Timestamp

6/15/2015, 12:51:19 AM

Confirmations

5,706,920

Merkle Root

70e3650410f946488401e5a677b50c7a8b826b93c169b6558547b8c01564c81c
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.

1.116 × 10⁹⁵(96-digit number)
11161436239402884993…84792432191827097599
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
1.116 × 10⁹⁵(96-digit number)
11161436239402884993…84792432191827097599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.232 × 10⁹⁵(96-digit number)
22322872478805769986…69584864383654195199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.464 × 10⁹⁵(96-digit number)
44645744957611539972…39169728767308390399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.929 × 10⁹⁵(96-digit number)
89291489915223079944…78339457534616780799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.785 × 10⁹⁶(97-digit number)
17858297983044615988…56678915069233561599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.571 × 10⁹⁶(97-digit number)
35716595966089231977…13357830138467123199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.143 × 10⁹⁶(97-digit number)
71433191932178463955…26715660276934246399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.428 × 10⁹⁷(98-digit number)
14286638386435692791…53431320553868492799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.857 × 10⁹⁷(98-digit number)
28573276772871385582…06862641107736985599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.714 × 10⁹⁷(98-digit number)
57146553545742771164…13725282215473971199
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:57,743,274 XPM·at block #6,812,405 · updates every 60s
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