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Block #2,778,788

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/4/2018, 12:10:11 PM Β· Difficulty 11.6500 Β· 4,066,202 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5aace983ba215de52c9c1e566252c91a3fe80493730a85986d4fa9fe0d4691ac
View on Chainz β†—

Height

#2,778,788

Difficulty

11.650010

Transactions

1

Size

200 B

Version

2

Bits

0ba6670a

Nonce

417,580,777

Timestamp

8/4/2018, 12:10:11 PM

Confirmations

4,066,202

Mined by

⛏️ P2SHAegGrGqMbFGVa2iMKocQEc7JUKPFP4ZQSe

Merkle Root

e3bb7295c2986e231122c9371644148afd7fd6ace5fd1c4b0861b0fd27e93f52
Transactions (1)
Coinbasee3bb7295c2986e…61b0fd27e93f52
1 in β†’ 1 out7.3600 XPM110 B
AegGrGqM…PFP4ZQSe
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.

2.560 Γ— 10⁹⁴(95-digit number)
25606794477166368792…93275495906829585861
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.560 Γ— 10⁹⁴(95-digit number)
25606794477166368792…93275495906829585861
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.121 Γ— 10⁹⁴(95-digit number)
51213588954332737585…86550991813659171721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.024 Γ— 10⁹⁡(96-digit number)
10242717790866547517…73101983627318343441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.048 Γ— 10⁹⁡(96-digit number)
20485435581733095034…46203967254636686881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.097 Γ— 10⁹⁡(96-digit number)
40970871163466190068…92407934509273373761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.194 Γ— 10⁹⁡(96-digit number)
81941742326932380136…84815869018546747521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.638 Γ— 10⁹⁢(97-digit number)
16388348465386476027…69631738037093495041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.277 Γ— 10⁹⁢(97-digit number)
32776696930772952054…39263476074186990081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.555 Γ— 10⁹⁢(97-digit number)
65553393861545904109…78526952148373980161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.311 Γ— 10⁹⁷(98-digit number)
13110678772309180821…57053904296747960321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.622 Γ— 10⁹⁷(98-digit number)
26221357544618361643…14107808593495920641
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:58,004,340 XPMΒ·at block #6,844,989 Β· updates every 60s
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