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Block #902,140

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/20/2015, 3:00:43 AM Β· Difficulty 10.9405 Β· 5,895,986 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2d88d86586502c139e6f5e3c9e722d135496c32c2d3e82a2f9eb2c32bcb80593
View on Chainz β†—

Height

#902,140

Difficulty

10.940516

Transactions

2

Size

1.43 KB

Version

2

Bits

0af0c5a8

Nonce

750,864,234

Timestamp

1/20/2015, 3:00:43 AM

Confirmations

5,895,986

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8e67f26b05ee5d4f93a9ca3ec85139cb0b51d8b7bcbe89f96af4888f719ad013
Transactions (2)
Coinbaseae28bb8d1b7f98…944c6d433de3a9
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
5d06fb406cdfc6…15a604f262b098
8 in β†’ 2 out1722.6702 XPM1.23 KB
AUSxVrre…B27XD3yvAJvuo6j3…hYYN9jCs
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.

3.939 Γ— 10⁹⁴(95-digit number)
39392911027644516760…21492407822786120319
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
3.939 Γ— 10⁹⁴(95-digit number)
39392911027644516760…21492407822786120319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.878 Γ— 10⁹⁴(95-digit number)
78785822055289033521…42984815645572240639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁡(96-digit number)
15757164411057806704…85969631291144481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.151 Γ— 10⁹⁡(96-digit number)
31514328822115613408…71939262582288962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.302 Γ— 10⁹⁡(96-digit number)
63028657644231226817…43878525164577925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁢(97-digit number)
12605731528846245363…87757050329155850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.521 Γ— 10⁹⁢(97-digit number)
25211463057692490726…75514100658311700479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.042 Γ— 10⁹⁢(97-digit number)
50422926115384981453…51028201316623400959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁷(98-digit number)
10084585223076996290…02056402633246801919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁷(98-digit number)
20169170446153992581…04112805266493603839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.033 Γ— 10⁹⁷(98-digit number)
40338340892307985163…08225610532987207679
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:57,629,012 XPMΒ·at block #6,798,125 Β· updates every 60s
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