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Block #172,659

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 10:06:51 AM Β· Difficulty 9.8618 Β· 6,643,209 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
69122740e8d7cc44389a505bdf58468e729460bcd1bfc760f4681bb350277ea2
View on Chainz β†—

Height

#172,659

Difficulty

9.861768

Transactions

1

Size

198 B

Version

2

Bits

09dc9cd0

Nonce

18,631

Timestamp

9/20/2013, 10:06:51 AM

Confirmations

6,643,209

Mined by

⛏️ P2SHAe6PYBDNs6MFPfqSfG8TyUUBAHjSQhB18y

Merkle Root

859173abf7efd411aa0accfacbb494ad50c33f981e067b0912aa35a01a4f70a6
Transactions (1)
Coinbase859173abf7efd4…aa35a01a4f70a6
1 in β†’ 1 out10.2700 XPM109 B
Ae6PYBDN…jSQhB18y
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.

7.800 Γ— 10⁹²(93-digit number)
78006180054000476027…24650691728722155841
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
7.800 Γ— 10⁹²(93-digit number)
78006180054000476027…24650691728722155841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.560 Γ— 10⁹³(94-digit number)
15601236010800095205…49301383457444311681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.120 Γ— 10⁹³(94-digit number)
31202472021600190410…98602766914888623361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.240 Γ— 10⁹³(94-digit number)
62404944043200380821…97205533829777246721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.248 Γ— 10⁹⁴(95-digit number)
12480988808640076164…94411067659554493441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.496 Γ— 10⁹⁴(95-digit number)
24961977617280152328…88822135319108986881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.992 Γ— 10⁹⁴(95-digit number)
49923955234560304657…77644270638217973761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.984 Γ— 10⁹⁴(95-digit number)
99847910469120609314…55288541276435947521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.996 Γ— 10⁹⁡(96-digit number)
19969582093824121862…10577082552871895041
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:57,771,057 XPMΒ·at block #6,815,867 Β· updates every 60s
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