Block #960,605

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/4/2015, 2:46:07 AM · Difficulty 10.8853 · 5,850,170 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
18780f5b13c6ea93ca90b1711f055db05a6cd72bbbfb6ab9a4da81f808b61488

Height

#960,605

Difficulty

10.885335

Transactions

5

Size

1.77 KB

Version

2

Bits

0ae2a54d

Nonce

484,904,998

Timestamp

3/4/2015, 2:46:07 AM

Confirmations

5,850,170

Merkle Root

2b51a23915ec32a9afc3c7bdce3cda8ba4de421286c1ed0c12e9bc7655ea8cdb
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.

1.232 × 10⁹⁶(97-digit number)
12327571286611300158…67355851896404462561
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
1.232 × 10⁹⁶(97-digit number)
12327571286611300158…67355851896404462561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.465 × 10⁹⁶(97-digit number)
24655142573222600316…34711703792808925121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.931 × 10⁹⁶(97-digit number)
49310285146445200632…69423407585617850241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.862 × 10⁹⁶(97-digit number)
98620570292890401265…38846815171235700481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.972 × 10⁹⁷(98-digit number)
19724114058578080253…77693630342471400961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.944 × 10⁹⁷(98-digit number)
39448228117156160506…55387260684942801921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.889 × 10⁹⁷(98-digit number)
78896456234312321012…10774521369885603841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.577 × 10⁹⁸(99-digit number)
15779291246862464202…21549042739771207681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.155 × 10⁹⁸(99-digit number)
31558582493724928405…43098085479542415361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.311 × 10⁹⁸(99-digit number)
63117164987449856810…86196170959084830721
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:57,730,296 XPM·at block #6,810,774 · updates every 60s
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