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Block #102,456

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 3:30:05 AM Β· Difficulty 9.4942 Β· 6,703,856 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6b89b8d8829d970e20b834abf62eb16ce110aa1ff0caf889f68a10fcc0a0a94
View on Chainz β†—

Height

#102,456

Difficulty

9.494182

Transactions

1

Size

200 B

Version

2

Bits

097e82bd

Nonce

30,059

Timestamp

8/7/2013, 3:30:05 AM

Confirmations

6,703,856

Mined by

⛏️ P2SHAZ29sR79QusQVNF36wMX1odggdnKVqwKGr

Merkle Root

7efb918e2e817870fb6cecccc8eb573563b899ae33d1508c967894d77ac8adc0
Transactions (1)
Coinbase7efb918e2e8178…7894d77ac8adc0
1 in β†’ 1 out11.0800 XPM109 B
AZ29sR79…nKVqwKGr
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.

2.015 Γ— 10⁹⁸(99-digit number)
20150230414152974925…08798613495574418449
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
2.015 Γ— 10⁹⁸(99-digit number)
20150230414152974925…08798613495574418449
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.030 Γ— 10⁹⁸(99-digit number)
40300460828305949850…17597226991148836899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.060 Γ— 10⁹⁸(99-digit number)
80600921656611899701…35194453982297673799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁹(100-digit number)
16120184331322379940…70388907964595347599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁹(100-digit number)
32240368662644759880…40777815929190695199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.448 Γ— 10⁹⁹(100-digit number)
64480737325289519760…81555631858381390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.289 Γ— 10¹⁰⁰(101-digit number)
12896147465057903952…63111263716762780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.579 Γ— 10¹⁰⁰(101-digit number)
25792294930115807904…26222527433525561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.158 Γ— 10¹⁰⁰(101-digit number)
51584589860231615808…52445054867051123199
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:57,694,584 XPMΒ·at block #6,806,311 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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