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Block #2,783,180

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2018, 10:45:29 AM Β· Difficulty 11.6608 Β· 4,058,650 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
edd3c8d9a3fef5fc82e9f90709eb6064b51c8df7b43ccc66e84525c67663f787
View on Chainz β†—

Height

#2,783,180

Difficulty

11.660844

Transactions

1

Size

200 B

Version

2

Bits

0ba92d0e

Nonce

688,228,730

Timestamp

8/7/2018, 10:45:29 AM

Confirmations

4,058,650

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

cf8fb9a2b9c27af740073cdc14fa2925f0d171cc2493cedda549c8b72aff3afd
Transactions (1)
Coinbasecf8fb9a2b9c27a…49c8b72aff3afd
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
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.

8.474 Γ— 10⁹⁴(95-digit number)
84749616801872216655…94807731821063577599
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
8.474 Γ— 10⁹⁴(95-digit number)
84749616801872216655…94807731821063577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.694 Γ— 10⁹⁡(96-digit number)
16949923360374443331…89615463642127155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.389 Γ— 10⁹⁡(96-digit number)
33899846720748886662…79230927284254310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.779 Γ— 10⁹⁡(96-digit number)
67799693441497773324…58461854568508620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.355 Γ— 10⁹⁢(97-digit number)
13559938688299554664…16923709137017241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.711 Γ— 10⁹⁢(97-digit number)
27119877376599109329…33847418274034483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.423 Γ— 10⁹⁢(97-digit number)
54239754753198218659…67694836548068966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁷(98-digit number)
10847950950639643731…35389673096137932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.169 Γ— 10⁹⁷(98-digit number)
21695901901279287463…70779346192275865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.339 Γ— 10⁹⁷(98-digit number)
43391803802558574927…41558692384551731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.678 Γ— 10⁹⁷(98-digit number)
86783607605117149854…83117384769103462399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,979,013 XPMΒ·at block #6,841,829 Β· updates every 60s
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