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Block #89,080

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/30/2013, 2:51:20 AM Β· Difficulty 9.2601 Β· 6,718,893 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1de58cb09ca3ea3a52c759d004fa26b07f2384622a48f784231d3566a95cdf1c
View on Chainz β†—

Height

#89,080

Difficulty

9.260136

Transactions

1

Size

204 B

Version

2

Bits

09429844

Nonce

107,545

Timestamp

7/30/2013, 2:51:20 AM

Confirmations

6,718,893

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

085b4ac3558e474a92216233fb2314e7b0781eeb59f730c8e2454aea82b09c8e
Transactions (1)
Coinbase085b4ac3558e47…454aea82b09c8e
1 in β†’ 1 out11.6500 XPM109 B
AdhmaJ1p…MhFRDjQ7
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.

2.342 Γ— 10¹⁰⁷(108-digit number)
23423124446699506839…84135418362393592799
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
2.342 Γ— 10¹⁰⁷(108-digit number)
23423124446699506839…84135418362393592799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.684 Γ— 10¹⁰⁷(108-digit number)
46846248893399013678…68270836724787185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.369 Γ— 10¹⁰⁷(108-digit number)
93692497786798027356…36541673449574371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.873 Γ— 10¹⁰⁸(109-digit number)
18738499557359605471…73083346899148742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.747 Γ— 10¹⁰⁸(109-digit number)
37476999114719210942…46166693798297484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.495 Γ— 10¹⁰⁸(109-digit number)
74953998229438421885…92333387596594969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.499 Γ— 10¹⁰⁹(110-digit number)
14990799645887684377…84666775193189939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.998 Γ— 10¹⁰⁹(110-digit number)
29981599291775368754…69333550386379878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.996 Γ— 10¹⁰⁹(110-digit number)
59963198583550737508…38667100772759756799
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:57,707,828 XPMΒ·at block #6,807,972 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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