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Block #2,069,417

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/13/2017, 2:31:17 PM Β· Difficulty 10.8571 Β· 4,768,945 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b29d776938e3797d3918711a630a2c86ec112b782c2e6d9943f595119b3c4d71
View on Chainz β†—

Height

#2,069,417

Difficulty

10.857145

Transactions

2

Size

392 B

Version

2

Bits

0adb6ddd

Nonce

1,674,146,978

Timestamp

4/13/2017, 2:31:17 PM

Confirmations

4,768,945

Mined by

⛏️ P2SHAGdKoRPtr2fsuys6eQ3a22oYdZQrzKGESb

Merkle Root

cecf3b646b46f217d82a1253e1c0914df8bf6d928f03a4a839e8c61ad5a99922
Transactions (2)
Coinbase3bfb28d1b85ce6…f679154cc8636d
1 in β†’ 1 out8.4800 XPM109 B
AGdKoRPt…QrzKGESb
1b3b4dbc53c8b0…6f56605191527d
1 in β†’ 1 out4999.9900 XPM192 B
Ada1dx2w…8gd1gZg2
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.

1.865 Γ— 10⁹⁷(98-digit number)
18654377686659061308…98935082523503083521
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
1.865 Γ— 10⁹⁷(98-digit number)
18654377686659061308…98935082523503083521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.730 Γ— 10⁹⁷(98-digit number)
37308755373318122616…97870165047006167041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.461 Γ— 10⁹⁷(98-digit number)
74617510746636245233…95740330094012334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.492 Γ— 10⁹⁸(99-digit number)
14923502149327249046…91480660188024668161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.984 Γ— 10⁹⁸(99-digit number)
29847004298654498093…82961320376049336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.969 Γ— 10⁹⁸(99-digit number)
59694008597308996186…65922640752098672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.193 Γ— 10⁹⁹(100-digit number)
11938801719461799237…31845281504197345281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.387 Γ— 10⁹⁹(100-digit number)
23877603438923598474…63690563008394690561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.775 Γ— 10⁹⁹(100-digit number)
47755206877847196949…27381126016789381121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.551 Γ— 10⁹⁹(100-digit number)
95510413755694393898…54762252033578762241
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:57,951,164 XPMΒ·at block #6,838,361 Β· updates every 60s
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