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Block #495,931

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/16/2014, 8:28:55 PM Β· Difficulty 10.7467 Β· 6,314,444 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
079becbd1b3e69642483011a0a9ff86d90fadcc1c14b6700ac6fa4bbbab767b4
View on Chainz β†—

Height

#495,931

Difficulty

10.746735

Transactions

2

Size

391 B

Version

2

Bits

0abf2a0e

Nonce

81,541

Timestamp

4/16/2014, 8:28:55 PM

Confirmations

6,314,444

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

84a47f3f153a28a3e5cc8b41f13ac8398c84c89aedfc49b66898670e9e41f325
Transactions (2)
Coinbasedd391a8e2ed010…acca54017d8127
1 in β†’ 1 out8.6500 XPM110 B
AeKNrjNj…1NEq95Ta
882258a34f9da6…fdda321614166f
1 in β†’ 1 out3.1945 XPM191 B
AZRPEac7…ixJb2qTx
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.

2.048 Γ— 10⁹⁴(95-digit number)
20486732784883063413…78888197176071595109
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
2.048 Γ— 10⁹⁴(95-digit number)
20486732784883063413…78888197176071595109
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.097 Γ— 10⁹⁴(95-digit number)
40973465569766126826…57776394352143190219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.194 Γ— 10⁹⁴(95-digit number)
81946931139532253653…15552788704286380439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.638 Γ— 10⁹⁡(96-digit number)
16389386227906450730…31105577408572760879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.277 Γ— 10⁹⁡(96-digit number)
32778772455812901461…62211154817145521759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.555 Γ— 10⁹⁡(96-digit number)
65557544911625802923…24422309634291043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.311 Γ— 10⁹⁢(97-digit number)
13111508982325160584…48844619268582087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.622 Γ— 10⁹⁢(97-digit number)
26223017964650321169…97689238537164174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.244 Γ— 10⁹⁢(97-digit number)
52446035929300642338…95378477074328348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁷(98-digit number)
10489207185860128467…90756954148656696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.097 Γ— 10⁹⁷(98-digit number)
20978414371720256935…81513908297313392639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,727,076 XPMΒ·at block #6,810,374 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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