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Block #85,505

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/27/2013, 11:47:13 AM Β· Difficulty 9.2899 Β· 6,713,944 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e169e0494c2929c0a8ceaac78ac736b7961329b8649dfac0c6c9b138db7d7c4
View on Chainz β†—

Height

#85,505

Difficulty

9.289874

Transactions

1

Size

199 B

Version

2

Bits

094a3529

Nonce

26,345

Timestamp

7/27/2013, 11:47:13 AM

Confirmations

6,713,944

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

a21d83e2d1d6eeaec717a85b9c814d21a363a79a47a3565e9e7a3fa1b95e393d
Transactions (1)
Coinbasea21d83e2d1d6ee…7a3fa1b95e393d
1 in β†’ 1 out11.5700 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.

9.074 Γ— 10⁹³(94-digit number)
90746233456262498385…60291023967471564449
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
9.074 Γ— 10⁹³(94-digit number)
90746233456262498385…60291023967471564449
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.814 Γ— 10⁹⁴(95-digit number)
18149246691252499677…20582047934943128899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.629 Γ— 10⁹⁴(95-digit number)
36298493382504999354…41164095869886257799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.259 Γ— 10⁹⁴(95-digit number)
72596986765009998708…82328191739772515599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.451 Γ— 10⁹⁡(96-digit number)
14519397353001999741…64656383479545031199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.903 Γ— 10⁹⁡(96-digit number)
29038794706003999483…29312766959090062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.807 Γ— 10⁹⁡(96-digit number)
58077589412007998966…58625533918180124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁢(97-digit number)
11615517882401599793…17251067836360249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.323 Γ— 10⁹⁢(97-digit number)
23231035764803199586…34502135672720499199
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:57,639,645 XPMΒ·at block #6,799,448 Β· updates every 60s
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