Block #3,017,456

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/20/2019, 8:23:02 AM · Difficulty 11.1687 · 3,824,572 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e080af0ccdde6b70fc81f019f64b55bb168b412d406d2d23e032b3c075ba8847

Height

#3,017,456

Difficulty

11.168741

Transactions

4

Size

1.86 KB

Version

2

Bits

0b2b32a0

Nonce

179,520,165

Timestamp

1/20/2019, 8:23:02 AM

Confirmations

3,824,572

Merkle Root

4c0d465542a5345841dc400944d0c31de3d2960857c560d9d08f8703b25fe0d2
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.

3.403 × 10⁹⁴(95-digit number)
34038387244607645494…53153155713714844881
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
3.403 × 10⁹⁴(95-digit number)
34038387244607645494…53153155713714844881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.807 × 10⁹⁴(95-digit number)
68076774489215290989…06306311427429689761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.361 × 10⁹⁵(96-digit number)
13615354897843058197…12612622854859379521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.723 × 10⁹⁵(96-digit number)
27230709795686116395…25225245709718759041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.446 × 10⁹⁵(96-digit number)
54461419591372232791…50450491419437518081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.089 × 10⁹⁶(97-digit number)
10892283918274446558…00900982838875036161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.178 × 10⁹⁶(97-digit number)
21784567836548893116…01801965677750072321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.356 × 10⁹⁶(97-digit number)
43569135673097786233…03603931355500144641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.713 × 10⁹⁶(97-digit number)
87138271346195572466…07207862711000289281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.742 × 10⁹⁷(98-digit number)
17427654269239114493…14415725422000578561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.485 × 10⁹⁷(98-digit number)
34855308538478228986…28831450844001157121
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,980,610 XPM·at block #6,842,027 · updates every 60s
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