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Block #73,114

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 3:59:53 AM Β· Difficulty 8.9946 Β· 6,730,558 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ee73489e3c76f73d88c6f94f7ff7e51e626f59c989e2887097ab97b86104a563
View on Chainz β†—

Height

#73,114

Difficulty

8.994590

Transactions

1

Size

199 B

Version

2

Bits

08fe9d70

Nonce

34

Timestamp

7/21/2013, 3:59:53 AM

Confirmations

6,730,558

Mined by

⛏️ P2SHALD4vzJs4Zwqrn14ZxtLe9UeDdGRCXP6ri

Merkle Root

c576a8df9018aa373db4c5d44db61b23455550773ec87f637ca9c2cb6d32c3b5
Transactions (1)
Coinbasec576a8df9018aa…a9c2cb6d32c3b5
1 in β†’ 1 out12.3400 XPM110 B
ALD4vzJs…GRCXP6ri
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.

8.653 Γ— 10⁹¹(92-digit number)
86539715263739447235…26571931609428421321
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
8.653 Γ— 10⁹¹(92-digit number)
86539715263739447235…26571931609428421321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.730 Γ— 10⁹²(93-digit number)
17307943052747889447…53143863218856842641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.461 Γ— 10⁹²(93-digit number)
34615886105495778894…06287726437713685281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.923 Γ— 10⁹²(93-digit number)
69231772210991557788…12575452875427370561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.384 Γ— 10⁹³(94-digit number)
13846354442198311557…25150905750854741121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.769 Γ— 10⁹³(94-digit number)
27692708884396623115…50301811501709482241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.538 Γ— 10⁹³(94-digit number)
55385417768793246230…00603623003418964481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.107 Γ— 10⁹⁴(95-digit number)
11077083553758649246…01207246006837928961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.215 Γ— 10⁹⁴(95-digit number)
22154167107517298492…02414492013675857921
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:57,673,412 XPMΒ·at block #6,803,671 Β· updates every 60s
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