Block #1,420,776

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/20/2016, 4:10:50 AM · Difficulty 10.7892 · 5,411,787 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c66b78cca70ff58137e104395c86e71f09def1f070481df2cf088725f4f49ba9

Height

#1,420,776

Difficulty

10.789193

Transactions

2

Size

764 B

Version

2

Bits

0aca0892

Nonce

328,610,098

Timestamp

1/20/2016, 4:10:50 AM

Confirmations

5,411,787

Merkle Root

f2dd8fc74324ff263b6019b6a91565393cda951ccb8fd0847f7061d8e084a13f
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.

1.999 × 10⁹³(94-digit number)
19999556864179123819…67899932880866722781
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
1.999 × 10⁹³(94-digit number)
19999556864179123819…67899932880866722781
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.999 × 10⁹³(94-digit number)
39999113728358247639…35799865761733445561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.999 × 10⁹³(94-digit number)
79998227456716495279…71599731523466891121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.599 × 10⁹⁴(95-digit number)
15999645491343299055…43199463046933782241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.199 × 10⁹⁴(95-digit number)
31999290982686598111…86398926093867564481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.399 × 10⁹⁴(95-digit number)
63998581965373196223…72797852187735128961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.279 × 10⁹⁵(96-digit number)
12799716393074639244…45595704375470257921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.559 × 10⁹⁵(96-digit number)
25599432786149278489…91191408750940515841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.119 × 10⁹⁵(96-digit number)
51198865572298556978…82382817501881031681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.023 × 10⁹⁶(97-digit number)
10239773114459711395…64765635003762063361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.047 × 10⁹⁶(97-digit number)
20479546228919422791…29531270007524126721
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,904,661 XPM·at block #6,832,562 · updates every 60s
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