Block #2,460,494

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/6/2018, 5:51:19 PM · Difficulty 10.9546 · 4,353,547 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a5e019f0b30b578900b58aa762591a51ef9ae08c56baef06b40e89097d1e1f9

Height

#2,460,494

Difficulty

10.954587

Transactions

2

Size

427 B

Version

2

Bits

0af45fc9

Nonce

224,342,033

Timestamp

1/6/2018, 5:51:19 PM

Confirmations

4,353,547

Merkle Root

981ae81341acd61840fd181ca8823880a8469bc6994131c60af3e39d428d1a96
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.

3.369 × 10⁹⁶(97-digit number)
33696621620051234998…32176409299982069759
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
3.369 × 10⁹⁶(97-digit number)
33696621620051234998…32176409299982069759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.739 × 10⁹⁶(97-digit number)
67393243240102469996…64352818599964139519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.347 × 10⁹⁷(98-digit number)
13478648648020493999…28705637199928279039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.695 × 10⁹⁷(98-digit number)
26957297296040987998…57411274399856558079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.391 × 10⁹⁷(98-digit number)
53914594592081975997…14822548799713116159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.078 × 10⁹⁸(99-digit number)
10782918918416395199…29645097599426232319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.156 × 10⁹⁸(99-digit number)
21565837836832790398…59290195198852464639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.313 × 10⁹⁸(99-digit number)
43131675673665580797…18580390397704929279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.626 × 10⁹⁸(99-digit number)
86263351347331161595…37160780795409858559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.725 × 10⁹⁹(100-digit number)
17252670269466232319…74321561590819717119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.450 × 10⁹⁹(100-digit number)
34505340538932464638…48643123181639434239
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:57,756,403 XPM·at block #6,814,040 · updates every 60s
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