Block #626,461

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/10/2014, 6:39:14 AM · Difficulty 10.9605 · 6,190,420 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
653fc90f515623ab0ea51babb7aef6d6d03a3fc4d1d07a574cd0105d1ff7a06f

Height

#626,461

Difficulty

10.960505

Transactions

1

Size

731 B

Version

2

Bits

0af5e3af

Nonce

90,805

Timestamp

7/10/2014, 6:39:14 AM

Confirmations

6,190,420

Merkle Root

408e855a30a6d584d140b87033d11d24cce616a648c0fde377e1c71957082ff4
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.

6.054 × 10⁹⁴(95-digit number)
60542672754668016343…12806740259974223179
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
6.054 × 10⁹⁴(95-digit number)
60542672754668016343…12806740259974223179
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.210 × 10⁹⁵(96-digit number)
12108534550933603268…25613480519948446359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.421 × 10⁹⁵(96-digit number)
24217069101867206537…51226961039896892719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.843 × 10⁹⁵(96-digit number)
48434138203734413074…02453922079793785439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.686 × 10⁹⁵(96-digit number)
96868276407468826148…04907844159587570879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.937 × 10⁹⁶(97-digit number)
19373655281493765229…09815688319175141759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.874 × 10⁹⁶(97-digit number)
38747310562987530459…19631376638350283519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.749 × 10⁹⁶(97-digit number)
77494621125975060919…39262753276700567039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.549 × 10⁹⁷(98-digit number)
15498924225195012183…78525506553401134079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.099 × 10⁹⁷(98-digit number)
30997848450390024367…57051013106802268159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
6.199 × 10⁹⁷(98-digit number)
61995696900780048735…14102026213604536319
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:57,779,087 XPM·at block #6,816,880 · updates every 60s
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