Block #1,460,670

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/17/2016, 2:14:35 AM · Difficulty 10.7772 · 5,380,438 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
844d109819fabeba93db596db6c81e0868d3ff2d6c074c0fcc411658606b44da

Height

#1,460,670

Difficulty

10.777152

Transactions

2

Size

427 B

Version

2

Bits

0ac6f36d

Nonce

1,551,466,175

Timestamp

2/17/2016, 2:14:35 AM

Confirmations

5,380,438

Merkle Root

859dc2a2a48feb0d9ee9d09524e4e502fc71691fdfaa2e2c94fa735fbad0b7b9
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.

6.058 × 10⁹⁷(98-digit number)
60582999997344196089…61497452105685053441
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
6.058 × 10⁹⁷(98-digit number)
60582999997344196089…61497452105685053441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.211 × 10⁹⁸(99-digit number)
12116599999468839217…22994904211370106881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.423 × 10⁹⁸(99-digit number)
24233199998937678435…45989808422740213761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.846 × 10⁹⁸(99-digit number)
48466399997875356871…91979616845480427521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.693 × 10⁹⁸(99-digit number)
96932799995750713742…83959233690960855041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.938 × 10⁹⁹(100-digit number)
19386559999150142748…67918467381921710081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.877 × 10⁹⁹(100-digit number)
38773119998300285497…35836934763843420161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.754 × 10⁹⁹(100-digit number)
77546239996600570994…71673869527686840321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.550 × 10¹⁰⁰(101-digit number)
15509247999320114198…43347739055373680641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.101 × 10¹⁰⁰(101-digit number)
31018495998640228397…86695478110747361281
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,973,230 XPM·at block #6,841,107 · updates every 60s
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