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Block #72,274

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 11:11:17 PM Β· Difficulty 8.9939 Β· 6,724,279 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f0996b4054e2dfb026f2f232b7d0ffe39e82ef8913a28cb7d6d913721aa04260
View on Chainz β†—

Height

#72,274

Difficulty

8.993943

Transactions

2

Size

1.13 KB

Version

2

Bits

08fe7310

Nonce

109

Timestamp

7/20/2013, 11:11:17 PM

Confirmations

6,724,279

Mined by

⛏️ P2SHAFtAoT5FMjDKbqQQCDo9Dow9FrM3aYYsAz

Merkle Root

384c7865d712b473c5f35f0b5c8b473c2b8f18a6eac9b4485cccc463c58ef116
Transactions (2)
Coinbase5cacfa13028a0a…f2abfdc02f79ef
1 in β†’ 1 out12.3500 XPM109 B
AFtAoT5F…M3aYYsAz
18a6d8b9a9047c…5d5635d984f837
8 in β†’ 1 out98.9000 XPM957 B
AWThhUX5…uhd1H2jp
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.

7.869 Γ— 10⁹⁷(98-digit number)
78692804970296250070…59611212802719634841
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
7.869 Γ— 10⁹⁷(98-digit number)
78692804970296250070…59611212802719634841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.573 Γ— 10⁹⁸(99-digit number)
15738560994059250014…19222425605439269681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.147 Γ— 10⁹⁸(99-digit number)
31477121988118500028…38444851210878539361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.295 Γ— 10⁹⁸(99-digit number)
62954243976237000056…76889702421757078721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.259 Γ— 10⁹⁹(100-digit number)
12590848795247400011…53779404843514157441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.518 Γ— 10⁹⁹(100-digit number)
25181697590494800022…07558809687028314881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.036 Γ— 10⁹⁹(100-digit number)
50363395180989600044…15117619374056629761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.007 Γ— 10¹⁰⁰(101-digit number)
10072679036197920008…30235238748113259521
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:57,616,422 XPMΒ·at block #6,796,552 Β· updates every 60s
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