Block #2,920,372

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/12/2018, 7:33:24 PM · Difficulty 11.3919 · 3,921,775 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e5907c8eb1c321adfccb453e87cbe1d1c393b57885e4ba432b56433bea32572

Height

#2,920,372

Difficulty

11.391949

Transactions

28

Size

7.82 KB

Version

2

Bits

0b6456c1

Nonce

1,173,860,373

Timestamp

11/12/2018, 7:33:24 PM

Confirmations

3,921,775

Merkle Root

7d2f84900ae135110b49a0b3ea163a24bdbbe71136b0eec04a3d579903a69043
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.

5.354 × 10⁹⁴(95-digit number)
53541512019916915894…89167641903141182959
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
5.354 × 10⁹⁴(95-digit number)
53541512019916915894…89167641903141182959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.070 × 10⁹⁵(96-digit number)
10708302403983383178…78335283806282365919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.141 × 10⁹⁵(96-digit number)
21416604807966766357…56670567612564731839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.283 × 10⁹⁵(96-digit number)
42833209615933532715…13341135225129463679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.566 × 10⁹⁵(96-digit number)
85666419231867065431…26682270450258927359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.713 × 10⁹⁶(97-digit number)
17133283846373413086…53364540900517854719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.426 × 10⁹⁶(97-digit number)
34266567692746826172…06729081801035709439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.853 × 10⁹⁶(97-digit number)
68533135385493652345…13458163602071418879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.370 × 10⁹⁷(98-digit number)
13706627077098730469…26916327204142837759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.741 × 10⁹⁷(98-digit number)
27413254154197460938…53832654408285675519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.482 × 10⁹⁷(98-digit number)
54826508308394921876…07665308816571351039
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:57,981,566 XPM·at block #6,842,146 · updates every 60s
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