Block #910,677

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/26/2015, 11:51:14 AM · Difficulty 10.9328 · 5,898,971 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fa3b34cd94dd29b6d730ae203cd75c94f072247127a31dae711689f7081e317

Height

#910,677

Difficulty

10.932822

Transactions

3

Size

1.83 KB

Version

2

Bits

0aeecd69

Nonce

821,796,701

Timestamp

1/26/2015, 11:51:14 AM

Confirmations

5,898,971

Merkle Root

9d3c83125550ba9fa10d59cef9016be8cca3ddcfe83781b4af14e5bfe352cb68
Transactions (3)
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.

4.719 × 10⁹⁵(96-digit number)
47198975959596559818…69608277401491008321
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
4.719 × 10⁹⁵(96-digit number)
47198975959596559818…69608277401491008321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.439 × 10⁹⁵(96-digit number)
94397951919193119637…39216554802982016641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.887 × 10⁹⁶(97-digit number)
18879590383838623927…78433109605964033281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.775 × 10⁹⁶(97-digit number)
37759180767677247855…56866219211928066561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.551 × 10⁹⁶(97-digit number)
75518361535354495710…13732438423856133121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.510 × 10⁹⁷(98-digit number)
15103672307070899142…27464876847712266241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.020 × 10⁹⁷(98-digit number)
30207344614141798284…54929753695424532481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.041 × 10⁹⁷(98-digit number)
60414689228283596568…09859507390849064961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.208 × 10⁹⁸(99-digit number)
12082937845656719313…19719014781698129921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.416 × 10⁹⁸(99-digit number)
24165875691313438627…39438029563396259841
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:57,721,264 XPM·at block #6,809,647 · updates every 60s
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