Block #910,091

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2015, 1:12:03 AM · Difficulty 10.9335 · 5,914,546 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16f084ccab82d26b1df048e8caef828a68091528fe0346a1d7c0135cb83f0da1

Height

#910,091

Difficulty

10.933516

Transactions

3

Size

772 B

Version

2

Bits

0aeefae0

Nonce

255,841,408

Timestamp

1/26/2015, 1:12:03 AM

Confirmations

5,914,546

Merkle Root

2328e757a5f58ed814e50f4fb67f4bf524e5debc216bc9fdf29c9f97d8885a75
Transactions (3)
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.

9.623 × 10⁹⁷(98-digit number)
96230298246217971344…91893614722474557439
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
9.623 × 10⁹⁷(98-digit number)
96230298246217971344…91893614722474557439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.924 × 10⁹⁸(99-digit number)
19246059649243594268…83787229444949114879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.849 × 10⁹⁸(99-digit number)
38492119298487188537…67574458889898229759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.698 × 10⁹⁸(99-digit number)
76984238596974377075…35148917779796459519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.539 × 10⁹⁹(100-digit number)
15396847719394875415…70297835559592919039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.079 × 10⁹⁹(100-digit number)
30793695438789750830…40595671119185838079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.158 × 10⁹⁹(100-digit number)
61587390877579501660…81191342238371676159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.231 × 10¹⁰⁰(101-digit number)
12317478175515900332…62382684476743352319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.463 × 10¹⁰⁰(101-digit number)
24634956351031800664…24765368953486704639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.926 × 10¹⁰⁰(101-digit number)
49269912702063601328…49530737906973409279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.853 × 10¹⁰⁰(101-digit number)
98539825404127202657…99061475813946818559
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:57,841,160 XPM·at block #6,824,636 · updates every 60s
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