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Block #90,300

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2013, 12:39:08 AM Β· Difficulty 9.2474 Β· 6,705,582 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c54b66bc5062c13d45fa42f3ea987673529a32022be624e68151c14cd32a6c27
View on Chainz β†—

Height

#90,300

Difficulty

9.247450

Transactions

2

Size

357 B

Version

2

Bits

093f58db

Nonce

41,505

Timestamp

7/31/2013, 12:39:08 AM

Confirmations

6,705,582

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

a5d9b39185ecdbf26a7c1d6447ef8578ea51c45400077beee421c1dcafde2575
Transactions (2)
Coinbasee533e48be8e2bb…dc16433d1b78cd
1 in β†’ 1 out11.6900 XPM109 B
ATe7tG7X…yczDSDEp
97a6fcca5f41ec…707a0b735e7a8c
1 in β†’ 1 out11.5700 XPM157 B
AdrZgAo5…aLTu4NiJ
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.

1.149 Γ— 10⁹⁷(98-digit number)
11492692781350805396…08749648741937101539
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
1.149 Γ— 10⁹⁷(98-digit number)
11492692781350805396…08749648741937101539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.298 Γ— 10⁹⁷(98-digit number)
22985385562701610793…17499297483874203079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.597 Γ— 10⁹⁷(98-digit number)
45970771125403221587…34998594967748406159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.194 Γ— 10⁹⁷(98-digit number)
91941542250806443175…69997189935496812319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.838 Γ— 10⁹⁸(99-digit number)
18388308450161288635…39994379870993624639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.677 Γ— 10⁹⁸(99-digit number)
36776616900322577270…79988759741987249279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.355 Γ— 10⁹⁸(99-digit number)
73553233800645154540…59977519483974498559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.471 Γ— 10⁹⁹(100-digit number)
14710646760129030908…19955038967948997119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.942 Γ— 10⁹⁹(100-digit number)
29421293520258061816…39910077935897994239
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:57,611,146 XPMΒ·at block #6,795,881 Β· updates every 60s
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