Block #914,369

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/29/2015, 8:07:10 AM · Difficulty 10.9273 · 5,897,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa684887551a256902d17673db0588c7f40110316a95d8f8db6d4bca979cb13f

Height

#914,369

Difficulty

10.927342

Transactions

2

Size

6.35 KB

Version

2

Bits

0aed6649

Nonce

2,113,467,950

Timestamp

1/29/2015, 8:07:10 AM

Confirmations

5,897,855

Merkle Root

645b3beaae381879ebc029e24d5135888cb62af90ea3f3899403cdd6f91e7c33
Transactions (2)
1 in → 1 out8.4300 XPM109 B
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.

6.988 × 10⁹⁴(95-digit number)
69880879027861994636…22404212670289507039
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
6.988 × 10⁹⁴(95-digit number)
69880879027861994636…22404212670289507039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.397 × 10⁹⁵(96-digit number)
13976175805572398927…44808425340579014079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.795 × 10⁹⁵(96-digit number)
27952351611144797854…89616850681158028159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.590 × 10⁹⁵(96-digit number)
55904703222289595709…79233701362316056319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.118 × 10⁹⁶(97-digit number)
11180940644457919141…58467402724632112639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.236 × 10⁹⁶(97-digit number)
22361881288915838283…16934805449264225279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.472 × 10⁹⁶(97-digit number)
44723762577831676567…33869610898528450559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.944 × 10⁹⁶(97-digit number)
89447525155663353135…67739221797056901119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.788 × 10⁹⁷(98-digit number)
17889505031132670627…35478443594113802239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.577 × 10⁹⁷(98-digit number)
35779010062265341254…70956887188227604479
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:57,741,807 XPM·at block #6,812,223 · updates every 60s
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