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Block #2,671,593

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/21/2018, 2:43:54 PM Β· Difficulty 11.6891 Β· 4,153,970 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
97f2d938fba7ee81e243c3bbda7e1b254716190b870825f729f3518855029cbe
View on Chainz β†—

Height

#2,671,593

Difficulty

11.689072

Transactions

2

Size

1018 B

Version

2

Bits

0bb0670a

Nonce

1,237,176,163

Timestamp

5/21/2018, 2:43:54 PM

Confirmations

4,153,970

Mined by

⛏️ P2SHAUj9Hpc89n7JsPn62aduZh2Btz5ASHuYNd

Merkle Root

cde1e6b0b29deadb2bf6584a5941a17e1d1eb6bae3ab3d7cd422f0c80002dacd
Transactions (2)
Coinbase770c80a4fa980d…79c6e3b0d53158
1 in β†’ 1 out7.3300 XPM110 B
AUj9Hpc8…5ASHuYNd
4cd66ae105e932…3d53905ea8223f
5 in β†’ 2 out10200.0100 XPM817 B
ASGZPJ3c…hdSkWTD3AY1sDSVW…AXQK9K95
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.

1.013 Γ— 10⁹⁢(97-digit number)
10139563164002903751…78588912338468906241
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
1.013 Γ— 10⁹⁢(97-digit number)
10139563164002903751…78588912338468906241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20279126328005807502…57177824676937812481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.055 Γ— 10⁹⁢(97-digit number)
40558252656011615005…14355649353875624961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.111 Γ— 10⁹⁢(97-digit number)
81116505312023230010…28711298707751249921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.622 Γ— 10⁹⁷(98-digit number)
16223301062404646002…57422597415502499841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.244 Γ— 10⁹⁷(98-digit number)
32446602124809292004…14845194831004999681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.489 Γ— 10⁹⁷(98-digit number)
64893204249618584008…29690389662009999361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.297 Γ— 10⁹⁸(99-digit number)
12978640849923716801…59380779324019998721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.595 Γ— 10⁹⁸(99-digit number)
25957281699847433603…18761558648039997441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.191 Γ— 10⁹⁸(99-digit number)
51914563399694867206…37523117296079994881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.038 Γ— 10⁹⁹(100-digit number)
10382912679938973441…75046234592159989761
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:57,848,605 XPMΒ·at block #6,825,562 Β· updates every 60s
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