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Block #937,759

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/15/2015, 4:52:09 PM Β· Difficulty 10.9009 Β· 5,858,236 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5bf88ca79e71947b163194336eb9665e4604fff8ced06a1e6e75720eb4e26b08
View on Chainz β†—

Height

#937,759

Difficulty

10.900924

Transactions

2

Size

2.01 KB

Version

2

Bits

0ae6a2f5

Nonce

541,641,376

Timestamp

2/15/2015, 4:52:09 PM

Confirmations

5,858,236

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4821c62d51dac39bd2397e4444536a3f8626a75c9a88c1b27d52242faa2de127
Transactions (2)
Coinbase64b0870236e1ee…6be30926e7190c
1 in β†’ 1 out8.4200 XPM116 B
ANSXnLY2…Sd25TjkD
67bc2f4597431d…fd878f5ce09d52
12 in β†’ 2 out288.4301 XPM1.81 KB
AKGbt1BH…6b1vPxPBAQ3SuyCM…AmNvneTb
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.

7.684 Γ— 10⁹³(94-digit number)
76846235061792747184…55122248280254256119
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
7.684 Γ— 10⁹³(94-digit number)
76846235061792747184…55122248280254256119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.536 Γ— 10⁹⁴(95-digit number)
15369247012358549436…10244496560508512239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.073 Γ— 10⁹⁴(95-digit number)
30738494024717098873…20488993121017024479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.147 Γ— 10⁹⁴(95-digit number)
61476988049434197747…40977986242034048959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.229 Γ— 10⁹⁡(96-digit number)
12295397609886839549…81955972484068097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.459 Γ— 10⁹⁡(96-digit number)
24590795219773679098…63911944968136195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.918 Γ— 10⁹⁡(96-digit number)
49181590439547358197…27823889936272391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.836 Γ— 10⁹⁡(96-digit number)
98363180879094716395…55647779872544783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.967 Γ— 10⁹⁢(97-digit number)
19672636175818943279…11295559745089566719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.934 Γ— 10⁹⁢(97-digit number)
39345272351637886558…22591119490179133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.869 Γ— 10⁹⁢(97-digit number)
78690544703275773116…45182238980358266879
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:57,612,049 XPMΒ·at block #6,795,994 Β· updates every 60s
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