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Block #448,919

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/18/2014, 6:38:37 AM Β· Difficulty 10.3655 Β· 6,352,567 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be58fbe38b9f80a7b68a2f1bf8c8110434b322f448c48caa125dab2bc33f4286
View on Chainz β†—

Height

#448,919

Difficulty

10.365514

Transactions

1

Size

200 B

Version

2

Bits

0a5d9257

Nonce

28,407

Timestamp

3/18/2014, 6:38:37 AM

Confirmations

6,352,567

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

a061e79cdf8c79bb9bc1e89f1c3feea77111b4d3d4af8441e0b7029749957839
Transactions (1)
Coinbasea061e79cdf8c79…b7029749957839
1 in β†’ 1 out9.2900 XPM109 B
AUm1UXE6…STx2UrXW
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.

2.035 Γ— 10⁹⁷(98-digit number)
20350010080978596012…24333889857891514639
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
2.035 Γ— 10⁹⁷(98-digit number)
20350010080978596012…24333889857891514639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.070 Γ— 10⁹⁷(98-digit number)
40700020161957192025…48667779715783029279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.140 Γ— 10⁹⁷(98-digit number)
81400040323914384050…97335559431566058559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.628 Γ— 10⁹⁸(99-digit number)
16280008064782876810…94671118863132117119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.256 Γ— 10⁹⁸(99-digit number)
32560016129565753620…89342237726264234239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.512 Γ— 10⁹⁸(99-digit number)
65120032259131507240…78684475452528468479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁹(100-digit number)
13024006451826301448…57368950905056936959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.604 Γ— 10⁹⁹(100-digit number)
26048012903652602896…14737901810113873919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.209 Γ— 10⁹⁹(100-digit number)
52096025807305205792…29475803620227747839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.041 Γ— 10¹⁰⁰(101-digit number)
10419205161461041158…58951607240455495679
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:57,655,958 XPMΒ·at block #6,801,485 Β· updates every 60s
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