Block #1,452,140

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/11/2016, 6:16:28 PM · Difficulty 10.7358 · 5,364,240 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f570a915d0d5ed0db25c7fdf58fd3e5be4a14e206ec53931e146eb6237d5a3c8

Height

#1,452,140

Difficulty

10.735820

Transactions

2

Size

3.71 KB

Version

2

Bits

0abc5eb1

Nonce

727,227,944

Timestamp

2/11/2016, 6:16:28 PM

Confirmations

5,364,240

Merkle Root

c4c8796fbfb5ce74470e690074d238a145df80bb298f07544c3c11c0d1a294dd
Transactions (2)
1 in → 1 out8.7000 XPM110 B
24 in → 1 out1.1054 XPM3.51 KB
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.

1.368 × 10⁹⁵(96-digit number)
13680906047444726849…01588505622342891521
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
1.368 × 10⁹⁵(96-digit number)
13680906047444726849…01588505622342891521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.736 × 10⁹⁵(96-digit number)
27361812094889453699…03177011244685783041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.472 × 10⁹⁵(96-digit number)
54723624189778907398…06354022489371566081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.094 × 10⁹⁶(97-digit number)
10944724837955781479…12708044978743132161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.188 × 10⁹⁶(97-digit number)
21889449675911562959…25416089957486264321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.377 × 10⁹⁶(97-digit number)
43778899351823125918…50832179914972528641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.755 × 10⁹⁶(97-digit number)
87557798703646251837…01664359829945057281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.751 × 10⁹⁷(98-digit number)
17511559740729250367…03328719659890114561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.502 × 10⁹⁷(98-digit number)
35023119481458500735…06657439319780229121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.004 × 10⁹⁷(98-digit number)
70046238962917001470…13314878639560458241
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:57,775,168 XPM·at block #6,816,379 · updates every 60s
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