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Block #3,475,970

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/14/2019, 9:09:42 PM Β· Difficulty 10.9790 Β· 3,330,349 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a74ff25c7da133d0771e3f8e9d014693c2167c78b324c65529a106e67e145336
View on Chainz β†—

Height

#3,475,970

Difficulty

10.979015

Transactions

2

Size

505 B

Version

2

Bits

0afaa0bf

Nonce

136,000,732

Timestamp

12/14/2019, 9:09:42 PM

Confirmations

3,330,349

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

fc6e2ee691580cacd69acd4d3ca75bc8abb541b92b94c68cf9e55167f8136467
Transactions (2)
Coinbase8ca94db9f20349…18cecc0119b68c
1 in β†’ 1 out8.2900 XPM110 B
ASiq2qtK…VMhmk7yL
cdf549ecf63502…bef4f438792d4b
2 in β†’ 2 out16.5500 XPM305 B
AbXhesW3…kBg97A7MALh3G4wq…cFPms2mF
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.

1.376 Γ— 10⁹⁴(95-digit number)
13763919153577011315…38074422023537051321
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.376 Γ— 10⁹⁴(95-digit number)
13763919153577011315…38074422023537051321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.752 Γ— 10⁹⁴(95-digit number)
27527838307154022631…76148844047074102641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.505 Γ— 10⁹⁴(95-digit number)
55055676614308045263…52297688094148205281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.101 Γ— 10⁹⁡(96-digit number)
11011135322861609052…04595376188296410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.202 Γ— 10⁹⁡(96-digit number)
22022270645723218105…09190752376592821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.404 Γ— 10⁹⁡(96-digit number)
44044541291446436210…18381504753185642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.808 Γ— 10⁹⁡(96-digit number)
88089082582892872421…36763009506371284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.761 Γ— 10⁹⁢(97-digit number)
17617816516578574484…73526019012742568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.523 Γ— 10⁹⁢(97-digit number)
35235633033157148968…47052038025485137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.047 Γ— 10⁹⁢(97-digit number)
70471266066314297937…94104076050970275841
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,694,634 XPMΒ·at block #6,806,318 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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