Block #1,463,945

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/19/2016, 8:30:23 AM · Difficulty 10.7781 · 5,353,272 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
62e29ecd880c7b107aa21f492b6a9ca2b413e444d6a41fcc50da1bcd17b9fe45

Height

#1,463,945

Difficulty

10.778103

Transactions

2

Size

5.76 KB

Version

2

Bits

0ac731bb

Nonce

161,078,272

Timestamp

2/19/2016, 8:30:23 AM

Confirmations

5,353,272

Merkle Root

015c8b35217f89a3326728d45b65f684b1220be447f5313e134d9e1f33eac62d
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.

1.186 × 10⁹⁴(95-digit number)
11866620363259161813…90710028980821085291
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
1.186 × 10⁹⁴(95-digit number)
11866620363259161813…90710028980821085291
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.373 × 10⁹⁴(95-digit number)
23733240726518323626…81420057961642170581
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.746 × 10⁹⁴(95-digit number)
47466481453036647253…62840115923284341161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.493 × 10⁹⁴(95-digit number)
94932962906073294506…25680231846568682321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.898 × 10⁹⁵(96-digit number)
18986592581214658901…51360463693137364641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.797 × 10⁹⁵(96-digit number)
37973185162429317802…02720927386274729281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.594 × 10⁹⁵(96-digit number)
75946370324858635605…05441854772549458561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.518 × 10⁹⁶(97-digit number)
15189274064971727121…10883709545098917121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.037 × 10⁹⁶(97-digit number)
30378548129943454242…21767419090197834241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.075 × 10⁹⁶(97-digit number)
60757096259886908484…43534838180395668481
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:57,781,774 XPM·at block #6,817,216 · updates every 60s
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