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Block #90,304

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2013, 12:43:28 AM Β· Difficulty 9.2471 Β· 6,712,341 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc218f775004e78dd9496730ca710aba8fe4e3a5e2a74b5e2cd6ed47c28b35b5
View on Chainz β†—

Height

#90,304

Difficulty

9.247096

Transactions

1

Size

204 B

Version

2

Bits

093f41b5

Nonce

24,255

Timestamp

7/31/2013, 12:43:28 AM

Confirmations

6,712,341

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

629ed4171a6fdd415c025027ffb8f51b3e9180e6f6bee62cde8a050e0da4888d
Transactions (1)
Coinbase629ed4171a6fdd…8a050e0da4888d
1 in β†’ 1 out11.6800 XPM109 B
ATe7tG7X…yczDSDEp
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.

3.301 Γ— 10¹⁰⁡(106-digit number)
33010906176525205568…45555029543719598059
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
3.301 Γ— 10¹⁰⁡(106-digit number)
33010906176525205568…45555029543719598059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.602 Γ— 10¹⁰⁡(106-digit number)
66021812353050411137…91110059087439196119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.320 Γ— 10¹⁰⁢(107-digit number)
13204362470610082227…82220118174878392239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.640 Γ— 10¹⁰⁢(107-digit number)
26408724941220164455…64440236349756784479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.281 Γ— 10¹⁰⁢(107-digit number)
52817449882440328910…28880472699513568959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.056 Γ— 10¹⁰⁷(108-digit number)
10563489976488065782…57760945399027137919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.112 Γ— 10¹⁰⁷(108-digit number)
21126979952976131564…15521890798054275839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.225 Γ— 10¹⁰⁷(108-digit number)
42253959905952263128…31043781596108551679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.450 Γ— 10¹⁰⁷(108-digit number)
84507919811904526256…62087563192217103359
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:57,665,176 XPMΒ·at block #6,802,644 Β· updates every 60s
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