Block #2,655,479

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/10/2018, 5:12:23 AM · Difficulty 11.7067 · 4,186,951 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ef3b36f7530c083258365cd884918794577a19ffdefea6a4e5615b17897ec91d

Height

#2,655,479

Difficulty

11.706689

Transactions

3

Size

3.09 KB

Version

2

Bits

0bb4e999

Nonce

265,211,865

Timestamp

5/10/2018, 5:12:23 AM

Confirmations

4,186,951

Merkle Root

9be1b2064f36239d8001aee0cdc0001b9d05e9a4f278559822e02fdfd59e8bdf
Transactions (3)
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.

3.105 × 10⁹⁴(95-digit number)
31058423782456832038…18777438364355340799
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
3.105 × 10⁹⁴(95-digit number)
31058423782456832038…18777438364355340799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.211 × 10⁹⁴(95-digit number)
62116847564913664077…37554876728710681599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.242 × 10⁹⁵(96-digit number)
12423369512982732815…75109753457421363199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.484 × 10⁹⁵(96-digit number)
24846739025965465631…50219506914842726399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.969 × 10⁹⁵(96-digit number)
49693478051930931262…00439013829685452799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.938 × 10⁹⁵(96-digit number)
99386956103861862524…00878027659370905599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.987 × 10⁹⁶(97-digit number)
19877391220772372504…01756055318741811199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.975 × 10⁹⁶(97-digit number)
39754782441544745009…03512110637483622399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.950 × 10⁹⁶(97-digit number)
79509564883089490019…07024221274967244799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.590 × 10⁹⁷(98-digit number)
15901912976617898003…14048442549934489599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.180 × 10⁹⁷(98-digit number)
31803825953235796007…28096885099868979199
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:57,983,855 XPM·at block #6,842,429 · updates every 60s
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