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Block #138,297

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/28/2013, 8:12:30 AM Β· Difficulty 9.8251 Β· 6,688,891 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
768ba8cb5620e896c4f8d42b3fddc00071b01ee47353e022cc3e21e183f1fd82
View on Chainz β†—

Height

#138,297

Difficulty

9.825130

Transactions

1

Size

199 B

Version

2

Bits

09d33bba

Nonce

15,874

Timestamp

8/28/2013, 8:12:30 AM

Confirmations

6,688,891

Mined by

⛏️ P2SHAW5bQGPKbBrq8V1mi9vfj96pi2goiqzYWr

Merkle Root

65efb285653c73acf204bc797f8a1fc75064fa138ebb25c24b818aea7c415f69
Transactions (1)
Coinbase65efb285653c73…818aea7c415f69
1 in β†’ 1 out10.3400 XPM109 B
AW5bQGPK…goiqzYWr
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.

1.828 Γ— 10⁹⁡(96-digit number)
18281849091145515096…32961403288250675199
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.828 Γ— 10⁹⁡(96-digit number)
18281849091145515096…32961403288250675199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.656 Γ— 10⁹⁡(96-digit number)
36563698182291030192…65922806576501350399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.312 Γ— 10⁹⁡(96-digit number)
73127396364582060385…31845613153002700799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.462 Γ— 10⁹⁢(97-digit number)
14625479272916412077…63691226306005401599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.925 Γ— 10⁹⁢(97-digit number)
29250958545832824154…27382452612010803199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.850 Γ— 10⁹⁢(97-digit number)
58501917091665648308…54764905224021606399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.170 Γ— 10⁹⁷(98-digit number)
11700383418333129661…09529810448043212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.340 Γ— 10⁹⁷(98-digit number)
23400766836666259323…19059620896086425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.680 Γ— 10⁹⁷(98-digit number)
46801533673332518646…38119241792172851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.360 Γ— 10⁹⁷(98-digit number)
93603067346665037293…76238483584345702399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,861,601 XPMΒ·at block #6,827,187 Β· updates every 60s
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