Block #840,617

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/5/2014, 7:00:00 AM · Difficulty 10.9742 · 5,964,557 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e217bca21b3633fcc3ad40ee2dbae254727ea26f52ed5b33a3a88b3993a1beff

Height

#840,617

Difficulty

10.974239

Transactions

5

Size

1.22 KB

Version

2

Bits

0af967b6

Nonce

1,007,904,454

Timestamp

12/5/2014, 7:00:00 AM

Confirmations

5,964,557

Merkle Root

0e2b006f8705c9ac8750b36d033275935d976fbceaf7b0441732254cc5d32504
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.

4.941 × 10⁹⁵(96-digit number)
49411278128567104253…19021515797165305601
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
4.941 × 10⁹⁵(96-digit number)
49411278128567104253…19021515797165305601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.882 × 10⁹⁵(96-digit number)
98822556257134208507…38043031594330611201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.976 × 10⁹⁶(97-digit number)
19764511251426841701…76086063188661222401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.952 × 10⁹⁶(97-digit number)
39529022502853683403…52172126377322444801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.905 × 10⁹⁶(97-digit number)
79058045005707366806…04344252754644889601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.581 × 10⁹⁷(98-digit number)
15811609001141473361…08688505509289779201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.162 × 10⁹⁷(98-digit number)
31623218002282946722…17377011018579558401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.324 × 10⁹⁷(98-digit number)
63246436004565893445…34754022037159116801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.264 × 10⁹⁸(99-digit number)
12649287200913178689…69508044074318233601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.529 × 10⁹⁸(99-digit number)
25298574401826357378…39016088148636467201
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:57,685,460 XPM·at block #6,805,173 · updates every 60s
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