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Block #39,116

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 12:59:50 PM Β· Difficulty 8.2783 Β· 6,767,631 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4f4fbb5c5027b0b8943edbfd7fd55f8cbd74cdc1f5885069b5776c6825b0e5d9
View on Chainz β†—

Height

#39,116

Difficulty

8.278323

Transactions

2

Size

358 B

Version

2

Bits

08474026

Nonce

24

Timestamp

7/14/2013, 12:59:50 PM

Confirmations

6,767,631

Mined by

⛏️ P2SHAaDPF1zGSyqhJb2BMFcTgE6zFSDs3aFGYB

Merkle Root

7ab91900c889ed5f76cbb3595d84a1e3ab8f5f0a010a1e26888e324c6a5ca83c
Transactions (2)
Coinbase35d1329730e385…59b8042312adfd
1 in β†’ 1 out14.5800 XPM110 B
AaDPF1zG…Ds3aFGYB
edb652ff5c4e91…876ee819dc72b6
1 in β†’ 1 out15.6200 XPM158 B
AVWm17kg…NLX81xfd
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.

7.728 Γ— 10⁹³(94-digit number)
77286831580865808245…24408242438261968401
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
7.728 Γ— 10⁹³(94-digit number)
77286831580865808245…24408242438261968401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.545 Γ— 10⁹⁴(95-digit number)
15457366316173161649…48816484876523936801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.091 Γ— 10⁹⁴(95-digit number)
30914732632346323298…97632969753047873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.182 Γ— 10⁹⁴(95-digit number)
61829465264692646596…95265939506095747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.236 Γ— 10⁹⁡(96-digit number)
12365893052938529319…90531879012191494401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.473 Γ— 10⁹⁡(96-digit number)
24731786105877058638…81063758024382988801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.946 Γ— 10⁹⁡(96-digit number)
49463572211754117276…62127516048765977601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.892 Γ— 10⁹⁡(96-digit number)
98927144423508234553…24255032097531955201
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:57,698,074 XPMΒ·at block #6,806,746 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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