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Block #161,433

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 4:04:52 PM Β· Difficulty 9.8594 Β· 6,633,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4947ece62c1404b68de5fd22ffc3f0a7fa98b95c374334b061ead6cd428290f9
View on Chainz β†—

Height

#161,433

Difficulty

9.859364

Transactions

1

Size

200 B

Version

2

Bits

09dbff41

Nonce

61,791

Timestamp

9/12/2013, 4:04:52 PM

Confirmations

6,633,445

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

16e51f0ee1bca917feee58cb4ecd57b0cf5ceedfceb1b0d0f16a7131ed9ed80e
Transactions (1)
Coinbase16e51f0ee1bca9…6a7131ed9ed80e
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.

7.878 Γ— 10⁹⁡(96-digit number)
78781722100470325068…68679340649308119041
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
7.878 Γ— 10⁹⁡(96-digit number)
78781722100470325068…68679340649308119041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.575 Γ— 10⁹⁢(97-digit number)
15756344420094065013…37358681298616238081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.151 Γ— 10⁹⁢(97-digit number)
31512688840188130027…74717362597232476161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.302 Γ— 10⁹⁢(97-digit number)
63025377680376260054…49434725194464952321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.260 Γ— 10⁹⁷(98-digit number)
12605075536075252010…98869450388929904641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.521 Γ— 10⁹⁷(98-digit number)
25210151072150504021…97738900777859809281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.042 Γ— 10⁹⁷(98-digit number)
50420302144301008043…95477801555719618561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.008 Γ— 10⁹⁸(99-digit number)
10084060428860201608…90955603111439237121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.016 Γ— 10⁹⁸(99-digit number)
20168120857720403217…81911206222878474241
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:57,603,058 XPMΒ·at block #6,794,877 Β· updates every 60s
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