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Block #2,657,120

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/11/2018, 5:06:10 PM Β· Difficulty 11.6753 Β· 4,185,669 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a8a332a5ed14a9c224ed7602a560ed328279dbf1b2d6bcc7b5b488ca1ab91367
View on Chainz β†—

Height

#2,657,120

Difficulty

11.675255

Transactions

3

Size

3.82 KB

Version

2

Bits

0bacdd87

Nonce

931,998,102

Timestamp

5/11/2018, 5:06:10 PM

Confirmations

4,185,669

Mined by

⛏️ P2SHAGe55K4baxB3HYB3n4C5QAVJ4p3jCVTDKX

Merkle Root

0c88954481ec95e7e257329976eeebf9aba758d974e83c56ee7dba346c4b1bad
Transactions (3)
Coinbase4356724afcb911…c0723de99cdd88
1 in β†’ 1 out7.3800 XPM109 B
AGe55K4b…3jCVTDKX
4d889846a580ee…07afa2bf3b9ecc
3 in β†’ 2 out3000.0142 XPM522 B
ALvotdMX…Em5NYjrWAPam1QKu…z5xJrsz1
e79a985cf32ecb…11cf54900c5a69
21 in β†’ 2 out80.4500 XPM3.11 KB
ARy5NTMV…6sh4Nb61AVyzKs82…Q85EQHvm
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.

8.892 Γ— 10⁹⁴(95-digit number)
88927352044012012951…65692894231693753121
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
8.892 Γ— 10⁹⁴(95-digit number)
88927352044012012951…65692894231693753121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.778 Γ— 10⁹⁡(96-digit number)
17785470408802402590…31385788463387506241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.557 Γ— 10⁹⁡(96-digit number)
35570940817604805180…62771576926775012481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.114 Γ— 10⁹⁡(96-digit number)
71141881635209610361…25543153853550024961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.422 Γ— 10⁹⁢(97-digit number)
14228376327041922072…51086307707100049921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.845 Γ— 10⁹⁢(97-digit number)
28456752654083844144…02172615414200099841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.691 Γ— 10⁹⁢(97-digit number)
56913505308167688288…04345230828400199681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.138 Γ— 10⁹⁷(98-digit number)
11382701061633537657…08690461656800399361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.276 Γ— 10⁹⁷(98-digit number)
22765402123267075315…17380923313600798721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.553 Γ— 10⁹⁷(98-digit number)
45530804246534150631…34761846627201597441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.106 Γ— 10⁹⁷(98-digit number)
91061608493068301262…69523693254403194881
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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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