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Block #37,213

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 10:22:40 AM Β· Difficulty 7.9960 Β· 6,772,601 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1fb8560bd574a3b0ba01c3b84f21c8a30b441ed512d0752ce442e2f90475a464
View on Chainz β†—

Height

#37,213

Difficulty

7.996011

Transactions

1

Size

199 B

Version

2

Bits

07fefa8f

Nonce

10

Timestamp

7/14/2013, 10:22:40 AM

Confirmations

6,772,601

Mined by

⛏️ P2SHAW3i3yVqzCnAxfabzgShSbqvKqQTovyczT

Merkle Root

e3df3f02a8004bc7b04d45d5893007ab9cc368fbd5bdd8efa8d69a3189f5bf9b
Transactions (1)
Coinbasee3df3f02a8004b…d69a3189f5bf9b
1 in β†’ 1 out15.6200 XPM109 B
AW3i3yVq…QTovyczT
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.

4.741 Γ— 10⁹⁴(95-digit number)
47416970028606136430…73043866049401523621
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
4.741 Γ— 10⁹⁴(95-digit number)
47416970028606136430…73043866049401523621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.483 Γ— 10⁹⁴(95-digit number)
94833940057212272861…46087732098803047241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.896 Γ— 10⁹⁡(96-digit number)
18966788011442454572…92175464197606094481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.793 Γ— 10⁹⁡(96-digit number)
37933576022884909144…84350928395212188961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.586 Γ— 10⁹⁡(96-digit number)
75867152045769818289…68701856790424377921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.517 Γ— 10⁹⁢(97-digit number)
15173430409153963657…37403713580848755841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.034 Γ— 10⁹⁢(97-digit number)
30346860818307927315…74807427161697511681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.069 Γ— 10⁹⁢(97-digit number)
60693721636615854631…49614854323395023361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,722,595 XPMΒ·at block #6,809,813 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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