Block #2,874,945

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 10/10/2018, 5:13:18 AM · Difficulty 11.6603 · 3,957,083 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d3b37d34c2c12eed6a5385717a519e6ce21db089a4a794c26bb7c403d4723d2e

Height

#2,874,945

Difficulty

11.660337

Transactions

2

Size

1.14 KB

Version

2

Bits

0ba90bdf

Nonce

239,506,470

Timestamp

10/10/2018, 5:13:18 AM

Confirmations

3,957,083

Merkle Root

b52bee0cf73aedc104a21268e7095f4eb00c76a8a4388e2d256e5d11f95ee7bc
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.

1.997 × 10⁹³(94-digit number)
19971015886539314065…48411729387989507669
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
1.997 × 10⁹³(94-digit number)
19971015886539314065…48411729387989507669
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.994 × 10⁹³(94-digit number)
39942031773078628130…96823458775979015339
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.988 × 10⁹³(94-digit number)
79884063546157256261…93646917551958030679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.597 × 10⁹⁴(95-digit number)
15976812709231451252…87293835103916061359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.195 × 10⁹⁴(95-digit number)
31953625418462902504…74587670207832122719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.390 × 10⁹⁴(95-digit number)
63907250836925805009…49175340415664245439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.278 × 10⁹⁵(96-digit number)
12781450167385161001…98350680831328490879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.556 × 10⁹⁵(96-digit number)
25562900334770322003…96701361662656981759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.112 × 10⁹⁵(96-digit number)
51125800669540644007…93402723325313963519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.022 × 10⁹⁶(97-digit number)
10225160133908128801…86805446650627927039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.045 × 10⁹⁶(97-digit number)
20450320267816257603…73610893301255854079
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:57,900,355 XPM·at block #6,832,027 · updates every 60s
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