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Block #933,515

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/12/2015, 5:16:04 PM Β· Difficulty 10.9017 Β· 5,868,720 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2da43924f0d3c81442faa8d0dea853ef874b8c0754a012b837f5eff1200ce279
View on Chainz β†—

Height

#933,515

Difficulty

10.901655

Transactions

2

Size

359 B

Version

2

Bits

0ae6d2d6

Nonce

1,436,852,842

Timestamp

2/12/2015, 5:16:04 PM

Confirmations

5,868,720

Mined by

⛏️ P2SHAenWMMgfDE7YAd4LtN9SztmLzrGQ7RN14F

Merkle Root

a9cd077dbf735d298354d658d0603e68a93c1001a876b3a13386e19ef83e9246
Transactions (2)
Coinbasef5bb3efd2bb208…b3e048746f9cba
1 in β†’ 1 out8.4100 XPM110 B
AenWMMgf…GQ7RN14F
1a9927caa106c6…7d5c69f09f8af8
1 in β†’ 1 out8.3900 XPM159 B
AekLq4Sw…ueWMfyir
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.

5.182 Γ— 10⁹³(94-digit number)
51825220421615549586…09216550928082111119
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.182 Γ— 10⁹³(94-digit number)
51825220421615549586…09216550928082111119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.036 Γ— 10⁹⁴(95-digit number)
10365044084323109917…18433101856164222239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.073 Γ— 10⁹⁴(95-digit number)
20730088168646219834…36866203712328444479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.146 Γ— 10⁹⁴(95-digit number)
41460176337292439668…73732407424656888959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.292 Γ— 10⁹⁴(95-digit number)
82920352674584879337…47464814849313777919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.658 Γ— 10⁹⁡(96-digit number)
16584070534916975867…94929629698627555839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.316 Γ— 10⁹⁡(96-digit number)
33168141069833951735…89859259397255111679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.633 Γ— 10⁹⁡(96-digit number)
66336282139667903470…79718518794510223359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.326 Γ— 10⁹⁢(97-digit number)
13267256427933580694…59437037589020446719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.653 Γ— 10⁹⁢(97-digit number)
26534512855867161388…18874075178040893439
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,661,888 XPMΒ·at block #6,802,234 Β· updates every 60s
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