Block #2,763,863

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/25/2018, 12:23:34 AM · Difficulty 11.6618 · 4,072,579 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6e0a47efd121bd721fc9889867503508f50d7aee5c99e9f0abc5782f886bb052

Height

#2,763,863

Difficulty

11.661850

Transactions

2

Size

723 B

Version

2

Bits

0ba96efe

Nonce

891,962,915

Timestamp

7/25/2018, 12:23:34 AM

Confirmations

4,072,579

Merkle Root

fd558a32631d2ff619d9447914c9dc9d2f407c9be39b5625afc6f8d16227e8f4
Transactions (2)
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.

9.622 × 10⁹⁴(95-digit number)
96222179432199828877…28476720694524359039
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
9.622 × 10⁹⁴(95-digit number)
96222179432199828877…28476720694524359039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.924 × 10⁹⁵(96-digit number)
19244435886439965775…56953441389048718079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.848 × 10⁹⁵(96-digit number)
38488871772879931551…13906882778097436159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.697 × 10⁹⁵(96-digit number)
76977743545759863102…27813765556194872319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.539 × 10⁹⁶(97-digit number)
15395548709151972620…55627531112389744639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.079 × 10⁹⁶(97-digit number)
30791097418303945240…11255062224779489279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.158 × 10⁹⁶(97-digit number)
61582194836607890481…22510124449558978559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.231 × 10⁹⁷(98-digit number)
12316438967321578096…45020248899117957119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.463 × 10⁹⁷(98-digit number)
24632877934643156192…90040497798235914239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.926 × 10⁹⁷(98-digit number)
49265755869286312385…80080995596471828479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.853 × 10⁹⁷(98-digit number)
98531511738572624770…60161991192943656959
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:57,935,806 XPM·at block #6,836,441 · updates every 60s
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