XPM Prime Explorer symbol
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Block #2,138,266

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/30/2017, 5:52:43 PM Β· Difficulty 10.8843 Β· 4,672,054 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
acfc9b20a535c27cb85deb04e6a058c07b4b225d07aede34d6f56a169e1fab21
View on Chainz β†—

Height

#2,138,266

Difficulty

10.884348

Transactions

2

Size

2.87 KB

Version

2

Bits

0ae264a9

Nonce

832,105,036

Timestamp

5/30/2017, 5:52:43 PM

Confirmations

4,672,054

Mined by

⛏️ P2SHAXELYK2AzJ45yamrtArgjKr3SNr5nR91Yy

Merkle Root

76b0c20806519c49a5edb7f46ac798b2915bbb28d5b3f1201fa0788aaa4ae79a
Transactions (2)
Coinbase643f9e3bb1a512…f48413bb8c634c
1 in β†’ 1 out8.4600 XPM109 B
AXELYK2A…r5nR91Yy
addb0ec36622c2…6e0eff0bffb7db
18 in β†’ 2 out34.9125 XPM2.68 KB
ALwoRk1n…iTUG5xsFAFuFH1pK…FZwcjzrq
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.

1.039 Γ— 10⁹⁡(96-digit number)
10395742414625564606…33370782652374901921
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
1.039 Γ— 10⁹⁡(96-digit number)
10395742414625564606…33370782652374901921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.079 Γ— 10⁹⁡(96-digit number)
20791484829251129213…66741565304749803841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.158 Γ— 10⁹⁡(96-digit number)
41582969658502258427…33483130609499607681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.316 Γ— 10⁹⁡(96-digit number)
83165939317004516854…66966261218999215361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.663 Γ— 10⁹⁢(97-digit number)
16633187863400903370…33932522437998430721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.326 Γ— 10⁹⁢(97-digit number)
33266375726801806741…67865044875996861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.653 Γ— 10⁹⁢(97-digit number)
66532751453603613483…35730089751993722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.330 Γ— 10⁹⁷(98-digit number)
13306550290720722696…71460179503987445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.661 Γ— 10⁹⁷(98-digit number)
26613100581441445393…42920359007974891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.322 Γ— 10⁹⁷(98-digit number)
53226201162882890786…85840718015949783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.064 Γ— 10⁹⁸(99-digit number)
10645240232576578157…71681436031899566081
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:57,726,638 XPMΒ·at block #6,810,319 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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