Block #911,698

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2015, 7:35:27 AM · Difficulty 10.9307 · 5,899,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
749c9db40b2edab3afa7d1cd23b5fab124c051426636dd27457157b0b18bee86

Height

#911,698

Difficulty

10.930654

Transactions

2

Size

2.00 KB

Version

2

Bits

0aee3f58

Nonce

280,930,210

Timestamp

1/27/2015, 7:35:27 AM

Confirmations

5,899,303

Merkle Root

91971d0a13251345a71c27af887188450423a142575bdda64a7ba35bec85a8b7
Transactions (2)
1 in → 1 out8.3900 XPM110 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.

7.234 × 10⁹²(93-digit number)
72349807032908261129…11492050467707395439
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
7.234 × 10⁹²(93-digit number)
72349807032908261129…11492050467707395439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.446 × 10⁹³(94-digit number)
14469961406581652225…22984100935414790879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.893 × 10⁹³(94-digit number)
28939922813163304451…45968201870829581759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.787 × 10⁹³(94-digit number)
57879845626326608903…91936403741659163519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.157 × 10⁹⁴(95-digit number)
11575969125265321780…83872807483318327039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.315 × 10⁹⁴(95-digit number)
23151938250530643561…67745614966636654079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.630 × 10⁹⁴(95-digit number)
46303876501061287122…35491229933273308159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.260 × 10⁹⁴(95-digit number)
92607753002122574245…70982459866546616319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.852 × 10⁹⁵(96-digit number)
18521550600424514849…41964919733093232639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.704 × 10⁹⁵(96-digit number)
37043101200849029698…83929839466186465279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.408 × 10⁹⁵(96-digit number)
74086202401698059396…67859678932372930559
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:57,732,111 XPM·at block #6,811,000 · updates every 60s
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