Block #3,372,457

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/28/2019, 7:34:03 AM · Difficulty 10.9948 · 3,464,060 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dbf5f07735788ed566ebe716be9dc1d71d27659b3486bdce829f56727e0ada94

Height

#3,372,457

Difficulty

10.994814

Transactions

2

Size

424 B

Version

2

Bits

0afeac26

Nonce

1,048,788,199

Timestamp

9/28/2019, 7:34:03 AM

Confirmations

3,464,060

Merkle Root

bf084f010513a554c5d87161202905d7a61d6e8750909d94f6e4c6bb558d8cac
Transactions (2)
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.

2.340 × 10⁹⁵(96-digit number)
23403714888938292201…59870645522948850241
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
2.340 × 10⁹⁵(96-digit number)
23403714888938292201…59870645522948850241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.680 × 10⁹⁵(96-digit number)
46807429777876584402…19741291045897700481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.361 × 10⁹⁵(96-digit number)
93614859555753168804…39482582091795400961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.872 × 10⁹⁶(97-digit number)
18722971911150633760…78965164183590801921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.744 × 10⁹⁶(97-digit number)
37445943822301267521…57930328367181603841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.489 × 10⁹⁶(97-digit number)
74891887644602535043…15860656734363207681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.497 × 10⁹⁷(98-digit number)
14978377528920507008…31721313468726415361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.995 × 10⁹⁷(98-digit number)
29956755057841014017…63442626937452830721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.991 × 10⁹⁷(98-digit number)
59913510115682028035…26885253874905661441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.198 × 10⁹⁸(99-digit number)
11982702023136405607…53770507749811322881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.396 × 10⁹⁸(99-digit number)
23965404046272811214…07541015499622645761
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,936,413 XPM·at block #6,836,516 · updates every 60s
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