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Block #147,049

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2013, 8:43:10 PM Β· Difficulty 9.8512 Β· 6,680,061 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91f005413010611b74d9ba5e61d9348840ee2c2850a85497cda1fc562d135184
View on Chainz β†—

Height

#147,049

Difficulty

9.851195

Transactions

2

Size

834 B

Version

2

Bits

09d9e7ed

Nonce

51,196

Timestamp

9/2/2013, 8:43:10 PM

Confirmations

6,680,061

Mined by

⛏️ P2SHAYkoKAQ4RDKGS7byjZXQArv3A5uuj8DeZs

Merkle Root

65fe8a387eb5c4e6fbca92297ef1572729e2e6f5a93baa576895eb24b5fd0621
Transactions (2)
Coinbasecaf030a3b98466…e322cc258735db
1 in β†’ 1 out10.3023 XPM109 B
AYkoKAQ4…uuj8DeZs
c4c16808174c07…27023b2077e453
4 in β†’ 1 out6.2400 XPM635 B
ARwRQL8j…mb3SXSrx
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.

2.007 Γ— 10⁹⁡(96-digit number)
20079656869327134085…00590315691591940001
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
2.007 Γ— 10⁹⁡(96-digit number)
20079656869327134085…00590315691591940001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.015 Γ— 10⁹⁡(96-digit number)
40159313738654268170…01180631383183880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.031 Γ— 10⁹⁡(96-digit number)
80318627477308536340…02361262766367760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.606 Γ— 10⁹⁢(97-digit number)
16063725495461707268…04722525532735520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.212 Γ— 10⁹⁢(97-digit number)
32127450990923414536…09445051065471040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.425 Γ— 10⁹⁢(97-digit number)
64254901981846829072…18890102130942080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.285 Γ— 10⁹⁷(98-digit number)
12850980396369365814…37780204261884160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.570 Γ— 10⁹⁷(98-digit number)
25701960792738731628…75560408523768320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.140 Γ— 10⁹⁷(98-digit number)
51403921585477463257…51120817047536640001
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:57,861,059 XPMΒ·at block #6,827,109 Β· updates every 60s
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