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Block #908,218

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/24/2015, 4:20:22 PM Β· Difficulty 10.9348 Β· 5,899,895 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5969dd24e160b8c4ce66b4c6d91c00fee99ca006b5d1e0a3a4c8d1963e88a714
View on Chainz β†—

Height

#908,218

Difficulty

10.934771

Transactions

2

Size

1.29 KB

Version

2

Bits

0aef4d25

Nonce

580,836,929

Timestamp

1/24/2015, 4:20:22 PM

Confirmations

5,899,895

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

682764a06b05593e945de2f7d5aa34d05ad018964ef28b749b41c055b3e42bb7
Transactions (2)
Coinbasefb8822e207bd5e…6f0459ff6f0276
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
0bdfe78617c324…434e2ca860de50
7 in β†’ 2 out587.0819 XPM1.08 KB
AcAFW717…V1pWEX3JARhTwwnA…h7UoJTbG
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.

1.302 Γ— 10⁹⁢(97-digit number)
13020020267002839940…72118666431135789499
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
1.302 Γ— 10⁹⁢(97-digit number)
13020020267002839940…72118666431135789499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.604 Γ— 10⁹⁢(97-digit number)
26040040534005679881…44237332862271578999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.208 Γ— 10⁹⁢(97-digit number)
52080081068011359762…88474665724543157999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.041 Γ— 10⁹⁷(98-digit number)
10416016213602271952…76949331449086315999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.083 Γ— 10⁹⁷(98-digit number)
20832032427204543905…53898662898172631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.166 Γ— 10⁹⁷(98-digit number)
41664064854409087810…07797325796345263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.332 Γ— 10⁹⁷(98-digit number)
83328129708818175620…15594651592690527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁸(99-digit number)
16665625941763635124…31189303185381055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.333 Γ— 10⁹⁸(99-digit number)
33331251883527270248…62378606370762111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.666 Γ— 10⁹⁸(99-digit number)
66662503767054540496…24757212741524223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.333 Γ— 10⁹⁹(100-digit number)
13332500753410908099…49514425483048447999
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:57,708,952 XPMΒ·at block #6,808,112 Β· updates every 60s
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