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Block #331,848

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/27/2013, 3:22:36 PM Β· Difficulty 10.1734 Β· 6,492,689 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
391e69b6a0f81b94a4b7ac9d92938e09784cb8805b85da92324b447e79f9cc2b
View on Chainz β†—

Height

#331,848

Difficulty

10.173435

Transactions

1

Size

207 B

Version

2

Bits

0a2c6638

Nonce

92,139

Timestamp

12/27/2013, 3:22:36 PM

Confirmations

6,492,689

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c7425e4cf84cb9b4846740a4f81ac12f2d0e500f25bbbf2ad2b98de8c20d34f5
Transactions (1)
Coinbasec7425e4cf84cb9…b98de8c20d34f5
1 in β†’ 1 out9.6500 XPM116 B
AbwWkWZt…kawDhufa
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.

4.813 Γ— 10⁹⁷(98-digit number)
48135462255845006442…18855581923649418239
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
4.813 Γ— 10⁹⁷(98-digit number)
48135462255845006442…18855581923649418239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.627 Γ— 10⁹⁷(98-digit number)
96270924511690012885…37711163847298836479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.925 Γ— 10⁹⁸(99-digit number)
19254184902338002577…75422327694597672959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.850 Γ— 10⁹⁸(99-digit number)
38508369804676005154…50844655389195345919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.701 Γ— 10⁹⁸(99-digit number)
77016739609352010308…01689310778390691839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁹(100-digit number)
15403347921870402061…03378621556781383679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.080 Γ— 10⁹⁹(100-digit number)
30806695843740804123…06757243113562767359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.161 Γ— 10⁹⁹(100-digit number)
61613391687481608246…13514486227125534719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.232 Γ— 10¹⁰⁰(101-digit number)
12322678337496321649…27028972454251069439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.464 Γ— 10¹⁰⁰(101-digit number)
24645356674992643298…54057944908502138879
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:57,840,358 XPMΒ·at block #6,824,536 Β· updates every 60s
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