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Block #74,725

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 12:34:48 PM Β· Difficulty 8.9957 Β· 6,731,619 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
64f6254b082d9f03b98fd09084c973e60ba68cdc76cfa150778fe9508f75dab3
View on Chainz β†—

Height

#74,725

Difficulty

8.995690

Transactions

1

Size

201 B

Version

2

Bits

08fee58a

Nonce

11

Timestamp

7/21/2013, 12:34:48 PM

Confirmations

6,731,619

Mined by

⛏️ P2SHAWMteqdVMhAhAkUuUfnMnzfAFbsGWCn49w

Merkle Root

0eecd79d348c9d60414ddfcc80b3bd7f571f2e0dfbae28a0805272f03ddb3bce
Transactions (1)
Coinbase0eecd79d348c9d…5272f03ddb3bce
1 in β†’ 1 out12.3400 XPM110 B
AWMteqdV…sGWCn49w
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.

1.149 Γ— 10⁹⁸(99-digit number)
11495023057477196023…12814000711411385521
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
1.149 Γ— 10⁹⁸(99-digit number)
11495023057477196023…12814000711411385521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.299 Γ— 10⁹⁸(99-digit number)
22990046114954392047…25628001422822771041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.598 Γ— 10⁹⁸(99-digit number)
45980092229908784095…51256002845645542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.196 Γ— 10⁹⁸(99-digit number)
91960184459817568191…02512005691291084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.839 Γ— 10⁹⁹(100-digit number)
18392036891963513638…05024011382582168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.678 Γ— 10⁹⁹(100-digit number)
36784073783927027276…10048022765164336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.356 Γ— 10⁹⁹(100-digit number)
73568147567854054553…20096045530328673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.471 Γ— 10¹⁰⁰(101-digit number)
14713629513570810910…40192091060657346561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.942 Γ— 10¹⁰⁰(101-digit number)
29427259027141621821…80384182121314693121
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:57,694,837 XPMΒ·at block #6,806,343 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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