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Block #162,568

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 9:46:13 AM Β· Difficulty 9.8614 Β· 6,644,303 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df678d516710f4cd806888bfeca2ef31af527e481fa35f96e37284345f86cc94
View on Chainz β†—

Height

#162,568

Difficulty

9.861443

Transactions

2

Size

1.57 KB

Version

2

Bits

09dc8789

Nonce

29,690

Timestamp

9/13/2013, 9:46:13 AM

Confirmations

6,644,303

Mined by

⛏️ P2SHAZVbBbt3ksoqjxYUuNvNpqh252D8XoJT8s

Merkle Root

0b926ba7d95588b27a7835bc1a9b1e05c0b2db2d80c4e0a3b292d363e74fa43a
Transactions (2)
Coinbased2b4c5788008e3…d24f6d27689184
1 in β†’ 1 out10.2900 XPM109 B
AZVbBbt3…D8XoJT8s
ef67f6325e282f…283476877d8b02
12 in β†’ 1 out123.1600 XPM1.38 KB
AQjAX9Vk…hTks6kYK
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.

2.809 Γ— 10⁹⁡(96-digit number)
28092387686698335273…09870772944200668801
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
2.809 Γ— 10⁹⁡(96-digit number)
28092387686698335273…09870772944200668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.618 Γ— 10⁹⁡(96-digit number)
56184775373396670546…19741545888401337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.123 Γ— 10⁹⁢(97-digit number)
11236955074679334109…39483091776802675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.247 Γ— 10⁹⁢(97-digit number)
22473910149358668218…78966183553605350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.494 Γ— 10⁹⁢(97-digit number)
44947820298717336437…57932367107210700801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.989 Γ— 10⁹⁢(97-digit number)
89895640597434672874…15864734214421401601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.797 Γ— 10⁹⁷(98-digit number)
17979128119486934574…31729468428842803201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.595 Γ— 10⁹⁷(98-digit number)
35958256238973869149…63458936857685606401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.191 Γ— 10⁹⁷(98-digit number)
71916512477947738299…26917873715371212801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,699,075 XPMΒ·at block #6,806,870 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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