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Block #2,833,399

1CCLength 13β˜…β˜…β˜…β˜…β˜…

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 5:15:23 PM Β· Difficulty 11.7161 Β· 4,009,150 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
63e8d52f059c05aafb87f8c26a95c19edf5a046e22fda3ef2a6d7b1070103350
View on Chainz β†—

Height

#2,833,399

Difficulty

11.716107

Transactions

1

Size

200 B

Version

2

Bits

0bb752c4

Nonce

949,453,574

Timestamp

9/10/2018, 5:15:23 PM

Confirmations

4,009,150

Mined by

⛏️ P2SHAGJ996cc2PqXTD4PcpEuknsJviW9QuAdun

Merkle Root

55f62b3e57a05feed52fe73f756dabaa2121cc6920a768c26842849bbb4f23d2
Transactions (1)
Coinbase55f62b3e57a05f…42849bbb4f23d2
1 in β†’ 1 out7.2700 XPM110 B
AGJ996cc…W9QuAdun
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.

1.508 Γ— 10⁹⁴(95-digit number)
15089466593431707547…51020925663118621339
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
1.508 Γ— 10⁹⁴(95-digit number)
15089466593431707547…51020925663118621339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.017 Γ— 10⁹⁴(95-digit number)
30178933186863415094…02041851326237242679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.035 Γ— 10⁹⁴(95-digit number)
60357866373726830189…04083702652474485359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.207 Γ— 10⁹⁡(96-digit number)
12071573274745366037…08167405304948970719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.414 Γ— 10⁹⁡(96-digit number)
24143146549490732075…16334810609897941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.828 Γ— 10⁹⁡(96-digit number)
48286293098981464151…32669621219795882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.657 Γ— 10⁹⁡(96-digit number)
96572586197962928303…65339242439591765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.931 Γ— 10⁹⁢(97-digit number)
19314517239592585660…30678484879183531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.862 Γ— 10⁹⁢(97-digit number)
38629034479185171321…61356969758367063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.725 Γ— 10⁹⁢(97-digit number)
77258068958370342642…22713939516734126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.545 Γ— 10⁹⁷(98-digit number)
15451613791674068528…45427879033468252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.090 Γ— 10⁹⁷(98-digit number)
30903227583348137056…90855758066936504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
13
2^12 Γ— origin βˆ’ 1
6.180 Γ— 10⁹⁷(98-digit number)
61806455166696274113…81711516133873008639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 13 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
LegendaryChain length 13

Roughly 1 in 100,000 blocks. Extremely rare β€” celebrated by the community.

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:57,984,817 XPMΒ·at block #6,842,548 Β· updates every 60s
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