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Block #174,372

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2013, 3:09:19 PM Β· Difficulty 9.8610 Β· 6,634,640 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
35cc98f775f9e7f4fb53831c640f317cb211a76de9dedaf54cd00fc038489603
View on Chainz β†—

Height

#174,372

Difficulty

9.861050

Transactions

1

Size

198 B

Version

2

Bits

09dc6dc0

Nonce

26,942

Timestamp

9/21/2013, 3:09:19 PM

Confirmations

6,634,640

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

351bde89350443c03eaccb00709b6c6598181264510a7ff562ec3720c1d407c3
Transactions (1)
Coinbase351bde89350443…ec3720c1d407c3
1 in β†’ 1 out10.2700 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

2.136 Γ— 10⁹²(93-digit number)
21361346771478079504…06933574493648562081
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
2.136 Γ— 10⁹²(93-digit number)
21361346771478079504…06933574493648562081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.272 Γ— 10⁹²(93-digit number)
42722693542956159008…13867148987297124161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.544 Γ— 10⁹²(93-digit number)
85445387085912318016…27734297974594248321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.708 Γ— 10⁹³(94-digit number)
17089077417182463603…55468595949188496641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.417 Γ— 10⁹³(94-digit number)
34178154834364927206…10937191898376993281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.835 Γ— 10⁹³(94-digit number)
68356309668729854413…21874383796753986561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.367 Γ— 10⁹⁴(95-digit number)
13671261933745970882…43748767593507973121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.734 Γ— 10⁹⁴(95-digit number)
27342523867491941765…87497535187015946241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.468 Γ— 10⁹⁴(95-digit number)
54685047734983883530…74995070374031892481
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:57,716,157 XPMΒ·at block #6,809,011 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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