Block #1,519,569

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/31/2016, 3:05:32 AM · Difficulty 10.5929 · 5,312,018 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bba2782497c255acc0ec3e614ca3776bc7f3432321a6ecffc6ebd932a36dc022

Height

#1,519,569

Difficulty

10.592914

Transactions

2

Size

1.14 KB

Version

2

Bits

0a97c938

Nonce

1,648,574,773

Timestamp

3/31/2016, 3:05:32 AM

Confirmations

5,312,018

Merkle Root

7a3a8b5aa1db9ee68f4730bb84cd89ccca79e35ffc13914e180be1705bcafe3c
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.

1.389 × 10⁹²(93-digit number)
13896160881689980746…38400819164402684521
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
1.389 × 10⁹²(93-digit number)
13896160881689980746…38400819164402684521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.779 × 10⁹²(93-digit number)
27792321763379961493…76801638328805369041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.558 × 10⁹²(93-digit number)
55584643526759922987…53603276657610738081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.111 × 10⁹³(94-digit number)
11116928705351984597…07206553315221476161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.223 × 10⁹³(94-digit number)
22233857410703969194…14413106630442952321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.446 × 10⁹³(94-digit number)
44467714821407938389…28826213260885904641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.893 × 10⁹³(94-digit number)
88935429642815876779…57652426521771809281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.778 × 10⁹⁴(95-digit number)
17787085928563175355…15304853043543618561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.557 × 10⁹⁴(95-digit number)
35574171857126350711…30609706087087237121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.114 × 10⁹⁴(95-digit number)
71148343714252701423…61219412174174474241
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:57,896,792 XPM·at block #6,831,586 · updates every 60s
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