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Block #1,578,098

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2016, 11:02:06 PM Β· Difficulty 10.6801 Β· 5,249,057 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76d5ac0c515ea3692ddfb0cf4ffa9ed01f9eedb1a80798691912a4a51b21de3f
View on Chainz β†—

Height

#1,578,098

Difficulty

10.680058

Transactions

1

Size

201 B

Version

2

Bits

0aae184c

Nonce

1,320,045,171

Timestamp

5/9/2016, 11:02:06 PM

Confirmations

5,249,057

Mined by

⛏️ P2SHARqcvS7XQtYDpViha71h3qYaCMKeKayx75

Merkle Root

8e4f7434f42c7755da16849901688d0c941d6d7ee0c77f83914573a5c99f3f3b
Transactions (1)
Coinbase8e4f7434f42c77…4573a5c99f3f3b
1 in β†’ 1 out8.7500 XPM110 B
ARqcvS7X…KeKayx75
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.

1.826 Γ— 10⁹⁢(97-digit number)
18265546435288712521…64117165116516730881
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
1.826 Γ— 10⁹⁢(97-digit number)
18265546435288712521…64117165116516730881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.653 Γ— 10⁹⁢(97-digit number)
36531092870577425042…28234330233033461761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.306 Γ— 10⁹⁢(97-digit number)
73062185741154850084…56468660466066923521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.461 Γ— 10⁹⁷(98-digit number)
14612437148230970016…12937320932133847041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.922 Γ— 10⁹⁷(98-digit number)
29224874296461940033…25874641864267694081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.844 Γ— 10⁹⁷(98-digit number)
58449748592923880067…51749283728535388161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.168 Γ— 10⁹⁸(99-digit number)
11689949718584776013…03498567457070776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.337 Γ— 10⁹⁸(99-digit number)
23379899437169552027…06997134914141552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.675 Γ— 10⁹⁸(99-digit number)
46759798874339104054…13994269828283105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.351 Γ— 10⁹⁸(99-digit number)
93519597748678208108…27988539656566210561
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:57,861,424 XPMΒ·at block #6,827,154 Β· updates every 60s
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