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Block #69,365

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 8:25:02 AM Β· Difficulty 8.9908 Β· 6,747,819 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f22c60fae256a0c3c414c59f5754e0fd61d2128e19670087809f6b192af862c8
View on Chainz β†—

Height

#69,365

Difficulty

8.990836

Transactions

2

Size

3.35 KB

Version

2

Bits

08fda769

Nonce

155

Timestamp

7/20/2013, 8:25:02 AM

Confirmations

6,747,819

Mined by

⛏️ P2SHAXibf3BjhoqdHBVzxvSXkbyS4CEe6Ywi6F

Merkle Root

8b11b8a483a79e55a1eb3b562170d1da98955a2c3e6f9baf246e7b031ff089ec
Transactions (2)
Coinbasecee1ef946e4c6a…03f6d1d29fbb1e
1 in β†’ 1 out12.3900 XPM110 B
AXibf3Bj…Ee6Ywi6F
74c142db8a3ec8…ba774374c0ab93
28 in β†’ 1 out391.7300 XPM3.16 KB
AJwja4yX…eWb3R1Pp
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.

1.283 Γ— 10⁸⁷(88-digit number)
12837934240410661975…65350646372902827501
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
1.283 Γ— 10⁸⁷(88-digit number)
12837934240410661975…65350646372902827501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.567 Γ— 10⁸⁷(88-digit number)
25675868480821323951…30701292745805655001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.135 Γ— 10⁸⁷(88-digit number)
51351736961642647902…61402585491611310001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.027 Γ— 10⁸⁸(89-digit number)
10270347392328529580…22805170983222620001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.054 Γ— 10⁸⁸(89-digit number)
20540694784657059161…45610341966445240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.108 Γ— 10⁸⁸(89-digit number)
41081389569314118322…91220683932890480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.216 Γ— 10⁸⁸(89-digit number)
82162779138628236644…82441367865780960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.643 Γ— 10⁸⁹(90-digit number)
16432555827725647328…64882735731561920001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,781,507 XPMΒ·at block #6,817,183 Β· updates every 60s
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