Block #912,994

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/28/2015, 8:41:23 AM · Difficulty 10.9277 · 5,901,918 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
adfca83691806943d2277c955954f10c972086b56129dab730ed2952e9b32ba5

Height

#912,994

Difficulty

10.927747

Transactions

7

Size

2.82 KB

Version

2

Bits

0aed80d8

Nonce

729,616,078

Timestamp

1/28/2015, 8:41:23 AM

Confirmations

5,901,918

Merkle Root

6fd2995241cffbf587c00013098e2c2cc3068e73fcdc439941b4588521afa455
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.

9.331 × 10⁹⁵(96-digit number)
93317958478810282778…39431139337582823681
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
9.331 × 10⁹⁵(96-digit number)
93317958478810282778…39431139337582823681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.866 × 10⁹⁶(97-digit number)
18663591695762056555…78862278675165647361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.732 × 10⁹⁶(97-digit number)
37327183391524113111…57724557350331294721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.465 × 10⁹⁶(97-digit number)
74654366783048226222…15449114700662589441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.493 × 10⁹⁷(98-digit number)
14930873356609645244…30898229401325178881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.986 × 10⁹⁷(98-digit number)
29861746713219290489…61796458802650357761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.972 × 10⁹⁷(98-digit number)
59723493426438580978…23592917605300715521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.194 × 10⁹⁸(99-digit number)
11944698685287716195…47185835210601431041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.388 × 10⁹⁸(99-digit number)
23889397370575432391…94371670421202862081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.777 × 10⁹⁸(99-digit number)
47778794741150864782…88743340842405724161
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:57,763,387 XPM·at block #6,814,911 · updates every 60s
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