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Block #162,654

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 11:13:51 AM Β· Difficulty 9.8614 Β· 6,633,420 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
93284024f9ba2d6fa82eb94f6f8169771b81a66b464895bd3de107658505094c
View on Chainz β†—

Height

#162,654

Difficulty

9.861404

Transactions

1

Size

198 B

Version

2

Bits

09dc84fe

Nonce

111,211

Timestamp

9/13/2013, 11:13:51 AM

Confirmations

6,633,420

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

7ca8bbcd7d658fa7a211d1fdeaf8c8c10854157ecbf1f6f929e631166ffb274a
Transactions (1)
Coinbase7ca8bbcd7d658f…e631166ffb274a
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

1.975 Γ— 10⁹³(94-digit number)
19754073929097125313…91736777588909109281
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
1.975 Γ— 10⁹³(94-digit number)
19754073929097125313…91736777588909109281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.950 Γ— 10⁹³(94-digit number)
39508147858194250626…83473555177818218561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.901 Γ— 10⁹³(94-digit number)
79016295716388501252…66947110355636437121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.580 Γ— 10⁹⁴(95-digit number)
15803259143277700250…33894220711272874241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.160 Γ— 10⁹⁴(95-digit number)
31606518286555400500…67788441422545748481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.321 Γ— 10⁹⁴(95-digit number)
63213036573110801001…35576882845091496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.264 Γ— 10⁹⁡(96-digit number)
12642607314622160200…71153765690182993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.528 Γ— 10⁹⁡(96-digit number)
25285214629244320400…42307531380365987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.057 Γ— 10⁹⁡(96-digit number)
50570429258488640801…84615062760731975681
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:57,612,688 XPMΒ·at block #6,796,073 Β· updates every 60s
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