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Block #80,495

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/24/2013, 4:54:10 AM Β· Difficulty 9.2497 Β· 6,725,190 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
56902dee1c92c40152c6e622cf8b53bd3a1a079e81c4df2a975f9a945a2ba81a
View on Chainz β†—

Height

#80,495

Difficulty

9.249678

Transactions

2

Size

2.16 KB

Version

2

Bits

093feae4

Nonce

705

Timestamp

7/24/2013, 4:54:10 AM

Confirmations

6,725,190

Mined by

⛏️ P2SHAJG5MM5rRVAKiLH46N8qXGVhBF9VXaBp6j

Merkle Root

30d38cb896c5e5d46b9c5f65f776e832a43bcf8588c54d41f13a5d8bcb747264
Transactions (2)
Coinbasee0590d4750a022…5d0f43b02ba6fc
1 in β†’ 1 out11.7000 XPM110 B
AJG5MM5r…9VXaBp6j
244db854c72329…f9734da0b3ee11
17 in β†’ 2 out264.3200 XPM1.97 KB
ASXBENay…4pQMNCg6AMh59oRV…GQxR3fik
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.

4.458 Γ— 10⁹⁢(97-digit number)
44581354929323636002…47009506046616346661
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
4.458 Γ— 10⁹⁢(97-digit number)
44581354929323636002…47009506046616346661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.916 Γ— 10⁹⁢(97-digit number)
89162709858647272005…94019012093232693321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.783 Γ— 10⁹⁷(98-digit number)
17832541971729454401…88038024186465386641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.566 Γ— 10⁹⁷(98-digit number)
35665083943458908802…76076048372930773281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.133 Γ— 10⁹⁷(98-digit number)
71330167886917817604…52152096745861546561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.426 Γ— 10⁹⁸(99-digit number)
14266033577383563520…04304193491723093121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.853 Γ— 10⁹⁸(99-digit number)
28532067154767127041…08608386983446186241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.706 Γ— 10⁹⁸(99-digit number)
57064134309534254083…17216773966892372481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.141 Γ— 10⁹⁹(100-digit number)
11412826861906850816…34433547933784744961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,689,561 XPMΒ·at block #6,805,684 Β· updates every 60s
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