Block #1,609,570

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/1/2016, 12:29:09 PM · Difficulty 10.6101 · 5,235,300 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0998bd877e86786473a567ca4adf079e14752d2936ed9a8b46aa7f42d9b1212d

Height

#1,609,570

Difficulty

10.610089

Transactions

2

Size

903 B

Version

2

Bits

0a9c2ec8

Nonce

805,844,070

Timestamp

6/1/2016, 12:29:09 PM

Confirmations

5,235,300

Merkle Root

156dd88b0ed597fcc51a2a3cf7801d75f92fdd78a830e9dd55d6159b4aa5a70e
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.

6.268 × 10⁹⁶(97-digit number)
62684237465228073747…96216499428806374401
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
6.268 × 10⁹⁶(97-digit number)
62684237465228073747…96216499428806374401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.253 × 10⁹⁷(98-digit number)
12536847493045614749…92432998857612748801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.507 × 10⁹⁷(98-digit number)
25073694986091229499…84865997715225497601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.014 × 10⁹⁷(98-digit number)
50147389972182458998…69731995430450995201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.002 × 10⁹⁸(99-digit number)
10029477994436491799…39463990860901990401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.005 × 10⁹⁸(99-digit number)
20058955988872983599…78927981721803980801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.011 × 10⁹⁸(99-digit number)
40117911977745967198…57855963443607961601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.023 × 10⁹⁸(99-digit number)
80235823955491934396…15711926887215923201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.604 × 10⁹⁹(100-digit number)
16047164791098386879…31423853774431846401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.209 × 10⁹⁹(100-digit number)
32094329582196773758…62847707548863692801
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:58,003,372 XPM·at block #6,844,869 · updates every 60s
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