Block #1,487,889

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2016, 8:08:10 PM · Difficulty 10.7174 · 5,353,686 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0faa35acdf20a61f291dc1b292bf8aa13e13574e33e155ff968ac3db4cc1b198

Height

#1,487,889

Difficulty

10.717411

Transactions

2

Size

1.64 KB

Version

2

Bits

0ab7a839

Nonce

151,974,127

Timestamp

3/7/2016, 8:08:10 PM

Confirmations

5,353,686

Merkle Root

596f0f1a4994366f41e766dc376bc0a0dec1a581b19d6172fef772b840a9c832
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.

1.040 × 10⁹⁵(96-digit number)
10408287171673975595…92760751109586387201
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
1.040 × 10⁹⁵(96-digit number)
10408287171673975595…92760751109586387201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.081 × 10⁹⁵(96-digit number)
20816574343347951191…85521502219172774401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.163 × 10⁹⁵(96-digit number)
41633148686695902383…71043004438345548801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.326 × 10⁹⁵(96-digit number)
83266297373391804766…42086008876691097601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.665 × 10⁹⁶(97-digit number)
16653259474678360953…84172017753382195201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.330 × 10⁹⁶(97-digit number)
33306518949356721906…68344035506764390401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.661 × 10⁹⁶(97-digit number)
66613037898713443812…36688071013528780801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.332 × 10⁹⁷(98-digit number)
13322607579742688762…73376142027057561601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.664 × 10⁹⁷(98-digit number)
26645215159485377525…46752284054115123201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.329 × 10⁹⁷(98-digit number)
53290430318970755050…93504568108230246401
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:57,976,985 XPM·at block #6,841,574 · updates every 60s
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