Block #920,412

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/2/2015, 10:51:58 PM · Difficulty 10.9184 · 5,878,860 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e46d4a906002afd46f14ac84d19253a562247e80f6bb06fbfd9125107e2f13df

Height

#920,412

Difficulty

10.918379

Transactions

5

Size

1009 B

Version

2

Bits

0aeb1ae2

Nonce

927,153,225

Timestamp

2/2/2015, 10:51:58 PM

Confirmations

5,878,860

Merkle Root

876abeeccc57ab9c5dc587570c1e21aff8cdb50ea398eb634ea3054bc3984f7f
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.

8.155 × 10⁹⁵(96-digit number)
81553975965685368834…44416562588199402801
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
8.155 × 10⁹⁵(96-digit number)
81553975965685368834…44416562588199402801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.631 × 10⁹⁶(97-digit number)
16310795193137073766…88833125176398805601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.262 × 10⁹⁶(97-digit number)
32621590386274147533…77666250352797611201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.524 × 10⁹⁶(97-digit number)
65243180772548295067…55332500705595222401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.304 × 10⁹⁷(98-digit number)
13048636154509659013…10665001411190444801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.609 × 10⁹⁷(98-digit number)
26097272309019318027…21330002822380889601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.219 × 10⁹⁷(98-digit number)
52194544618038636054…42660005644761779201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.043 × 10⁹⁸(99-digit number)
10438908923607727210…85320011289523558401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.087 × 10⁹⁸(99-digit number)
20877817847215454421…70640022579047116801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.175 × 10⁹⁸(99-digit number)
41755635694430908843…41280045158094233601
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:57,638,216 XPM·at block #6,799,271 · updates every 60s
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