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Block #82,889

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2013, 6:11:51 PM Β· Difficulty 9.2729 Β· 6,716,391 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
426080222e0000db39d8925713839ec75497cc8d74e1dddb4f98da4d875f59a1
View on Chainz β†—

Height

#82,889

Difficulty

9.272890

Transactions

2

Size

836 B

Version

2

Bits

0945dc1f

Nonce

84,234

Timestamp

7/25/2013, 6:11:51 PM

Confirmations

6,716,391

Mined by

⛏️ P2SHAMFNaPSQ4Nph5v875H2AjwSTnK4SGs4TKn

Merkle Root

98923f0c1e7870f7a65e1faec3f4696831cb66b441ab579cce944651ffa8b571
Transactions (2)
Coinbasea37f031143659e…75aa65dd42f071
1 in β†’ 1 out11.6200 XPM109 B
AMFNaPSQ…4SGs4TKn
d7257508a9c671…4109bde7049f6c
4 in β†’ 1 out48.1200 XPM637 B
AWvvyEJH…DAk9m4bZ
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.

6.964 Γ— 10⁹⁡(96-digit number)
69649832225746822583…89083106259447465599
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
6.964 Γ— 10⁹⁡(96-digit number)
69649832225746822583…89083106259447465599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁢(97-digit number)
13929966445149364516…78166212518894931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.785 Γ— 10⁹⁢(97-digit number)
27859932890298729033…56332425037789862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.571 Γ— 10⁹⁢(97-digit number)
55719865780597458067…12664850075579724799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁷(98-digit number)
11143973156119491613…25329700151159449599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁷(98-digit number)
22287946312238983226…50659400302318899199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.457 Γ— 10⁹⁷(98-digit number)
44575892624477966453…01318800604637798399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.915 Γ— 10⁹⁷(98-digit number)
89151785248955932907…02637601209275596799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.783 Γ— 10⁹⁸(99-digit number)
17830357049791186581…05275202418551193599
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:57,638,281 XPMΒ·at block #6,799,279 Β· updates every 60s
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