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Block #28,537

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 12:37:05 PM Β· Difficulty 7.9822 Β· 6,766,453 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3d681ec70496d4472cffff85975fd5076f64e897bccea04e38d86d2e5db834b3
View on Chainz β†—

Height

#28,537

Difficulty

7.982210

Transactions

1

Size

202 B

Version

2

Bits

07fb7219

Nonce

1,109

Timestamp

7/13/2013, 12:37:05 PM

Confirmations

6,766,453

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

327c3a5c15256484d6603c093b762b20d88f9f5c45a7ad2785f46e0f8074d72d
Transactions (1)
Coinbase327c3a5c152564…f46e0f8074d72d
1 in β†’ 1 out15.6700 XPM108 B
AGemJXng…w1K3MEut
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.

1.863 Γ— 10¹⁰⁴(105-digit number)
18635629169842797118…01103818535354465901
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
1.863 Γ— 10¹⁰⁴(105-digit number)
18635629169842797118…01103818535354465901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.727 Γ— 10¹⁰⁴(105-digit number)
37271258339685594237…02207637070708931801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.454 Γ— 10¹⁰⁴(105-digit number)
74542516679371188475…04415274141417863601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.490 Γ— 10¹⁰⁡(106-digit number)
14908503335874237695…08830548282835727201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.981 Γ— 10¹⁰⁡(106-digit number)
29817006671748475390…17661096565671454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.963 Γ— 10¹⁰⁡(106-digit number)
59634013343496950780…35322193131342908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.192 Γ— 10¹⁰⁢(107-digit number)
11926802668699390156…70644386262685817601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,603,961 XPMΒ·at block #6,794,989 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK