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Block #2,132,807

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2017, 1:28:14 AM Β· Difficulty 10.9102 Β· 4,709,637 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9cca06051a15a4d48649b6a68e36ede681eab457629defdbfcd63d690532e79
View on Chainz β†—

Height

#2,132,807

Difficulty

10.910228

Transactions

1

Size

199 B

Version

2

Bits

0ae904ae

Nonce

1,517,490,689

Timestamp

5/26/2017, 1:28:14 AM

Confirmations

4,709,637

Mined by

⛏️ P2SHARK3f9QcEd7M7BuaQK571pGcwRF8ciF5eV

Merkle Root

c2b7ec93e315e440ff802814f619922f0d1b2fe27b0d4596c64a9472ae63cc2e
Transactions (1)
Coinbasec2b7ec93e315e4…4a9472ae63cc2e
1 in β†’ 1 out8.3900 XPM109 B
ARK3f9Qc…F8ciF5eV
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.417 Γ— 10⁹⁴(95-digit number)
34172592632732472649…32815072109727606079
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.417 Γ— 10⁹⁴(95-digit number)
34172592632732472649…32815072109727606079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.834 Γ— 10⁹⁴(95-digit number)
68345185265464945298…65630144219455212159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.366 Γ— 10⁹⁡(96-digit number)
13669037053092989059…31260288438910424319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.733 Γ— 10⁹⁡(96-digit number)
27338074106185978119…62520576877820848639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.467 Γ— 10⁹⁡(96-digit number)
54676148212371956238…25041153755641697279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁢(97-digit number)
10935229642474391247…50082307511283394559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.187 Γ— 10⁹⁢(97-digit number)
21870459284948782495…00164615022566789119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.374 Γ— 10⁹⁢(97-digit number)
43740918569897564991…00329230045133578239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.748 Γ— 10⁹⁢(97-digit number)
87481837139795129982…00658460090267156479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.749 Γ— 10⁹⁷(98-digit number)
17496367427959025996…01316920180534312959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,983,968 XPMΒ·at block #6,842,443 Β· updates every 60s
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