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Block #152,906

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2013, 3:33:09 PM Β· Difficulty 9.8630 Β· 6,641,745 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
27331be81928a99fdb9d411545a1c62933ea206879294f279e4af5aac5c2b4c8
View on Chainz β†—

Height

#152,906

Difficulty

9.862984

Transactions

2

Size

1.80 KB

Version

2

Bits

09dcec8a

Nonce

3,395

Timestamp

9/6/2013, 3:33:09 PM

Confirmations

6,641,745

Mined by

⛏️ P2SHAGYgfxeDe54JitukEoBoj169rmyzunm3ZL

Merkle Root

9077f45c10f19cbdd7d7a0d3cac3f3566390fc1e9dfec0f71f070c99b38790c1
Transactions (2)
Coinbasefc68da522315f3…47b73d31d3ef8e
1 in β†’ 1 out10.2800 XPM109 B
AGYgfxeD…yzunm3ZL
58d893e89e800a…664eb429ff2802
14 in β†’ 1 out144.0300 XPM1.61 KB
AJs27LEf…M76myr9t
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.

1.740 Γ— 10⁹³(94-digit number)
17408284558426742299…73833029698229386561
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
1.740 Γ— 10⁹³(94-digit number)
17408284558426742299…73833029698229386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.481 Γ— 10⁹³(94-digit number)
34816569116853484598…47666059396458773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.963 Γ— 10⁹³(94-digit number)
69633138233706969197…95332118792917546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.392 Γ— 10⁹⁴(95-digit number)
13926627646741393839…90664237585835092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.785 Γ— 10⁹⁴(95-digit number)
27853255293482787679…81328475171670184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.570 Γ— 10⁹⁴(95-digit number)
55706510586965575358…62656950343340369921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.114 Γ— 10⁹⁡(96-digit number)
11141302117393115071…25313900686680739841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.228 Γ— 10⁹⁡(96-digit number)
22282604234786230143…50627801373361479681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.456 Γ— 10⁹⁡(96-digit number)
44565208469572460286…01255602746722959361
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:57,601,257 XPMΒ·at block #6,794,650 Β· updates every 60s
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