Block #786,620

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 10/28/2014, 11:18:00 AM · Difficulty 10.9748 · 6,012,910 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1536c97bc4d4c730cc8a960c88ab1a32f04e7f8fbca4d41278b2941866eac0a9

Height

#786,620

Difficulty

10.974768

Transactions

4

Size

2.60 KB

Version

2

Bits

0af98a65

Nonce

566,833,088

Timestamp

10/28/2014, 11:18:00 AM

Confirmations

6,012,910

Merkle Root

8994a1f11ab3715a8c2c7b8dc5bda9418a8042f0e7ec9e82db3ba9ce64196fb1
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.

6.153 × 10⁹⁵(96-digit number)
61536012401726741742…60746841005704784639
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
6.153 × 10⁹⁵(96-digit number)
61536012401726741742…60746841005704784639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.230 × 10⁹⁶(97-digit number)
12307202480345348348…21493682011409569279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.461 × 10⁹⁶(97-digit number)
24614404960690696697…42987364022819138559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.922 × 10⁹⁶(97-digit number)
49228809921381393394…85974728045638277119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.845 × 10⁹⁶(97-digit number)
98457619842762786788…71949456091276554239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.969 × 10⁹⁷(98-digit number)
19691523968552557357…43898912182553108479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.938 × 10⁹⁷(98-digit number)
39383047937105114715…87797824365106216959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.876 × 10⁹⁷(98-digit number)
78766095874210229430…75595648730212433919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.575 × 10⁹⁸(99-digit number)
15753219174842045886…51191297460424867839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.150 × 10⁹⁸(99-digit number)
31506438349684091772…02382594920849735679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
6.301 × 10⁹⁸(99-digit number)
63012876699368183544…04765189841699471359
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:57,640,290 XPM·at block #6,799,529 · updates every 60s
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