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Block #89,055

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/30/2013, 2:26:08 AM Β· Difficulty 9.2603 Β· 6,707,757 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
857a7cc435eefcd1895f1f318f013fda615a21feca7f033f1b27602d5cf59d60
View on Chainz β†—

Height

#89,055

Difficulty

9.260291

Transactions

1

Size

204 B

Version

2

Bits

0942a273

Nonce

318,995

Timestamp

7/30/2013, 2:26:08 AM

Confirmations

6,707,757

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

5c4986e5e453d380ea6b7da3bba5f5d9423f617bab68ab8c2867a34d4db457a7
Transactions (1)
Coinbase5c4986e5e453d3…67a34d4db457a7
1 in β†’ 1 out11.6400 XPM109 B
ATzEHZ7a…2eAGweip
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.

9.907 Γ— 10¹⁰⁢(107-digit number)
99070382180978648744…70182161708474707339
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
9.907 Γ— 10¹⁰⁢(107-digit number)
99070382180978648744…70182161708474707339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.981 Γ— 10¹⁰⁷(108-digit number)
19814076436195729748…40364323416949414679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.962 Γ— 10¹⁰⁷(108-digit number)
39628152872391459497…80728646833898829359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.925 Γ— 10¹⁰⁷(108-digit number)
79256305744782918995…61457293667797658719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.585 Γ— 10¹⁰⁸(109-digit number)
15851261148956583799…22914587335595317439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.170 Γ— 10¹⁰⁸(109-digit number)
31702522297913167598…45829174671190634879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.340 Γ— 10¹⁰⁸(109-digit number)
63405044595826335196…91658349342381269759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.268 Γ— 10¹⁰⁹(110-digit number)
12681008919165267039…83316698684762539519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.536 Γ— 10¹⁰⁹(110-digit number)
25362017838330534078…66633397369525079039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,618,511 XPMΒ·at block #6,796,811 Β· updates every 60s
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