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Block #70,612

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 2:32:32 PM Β· Difficulty 8.9923 Β· 6,739,345 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
db9adf00d10212217e282ce30baae2d26a5d011a722ff428aedc439e803b0d9a
View on Chainz β†—

Height

#70,612

Difficulty

8.992337

Transactions

1

Size

198 B

Version

2

Bits

08fe09cb

Nonce

553

Timestamp

7/20/2013, 2:32:32 PM

Confirmations

6,739,345

Mined by

⛏️ P2SHAGc7t72tWhbXJhPuYW3tRVfCU5UnvYxLPB

Merkle Root

6c6340dad1f03a74506e45e68eba144460edb9318f9ea4d7213d5a3ce188cb6b
Transactions (1)
Coinbase6c6340dad1f03a…3d5a3ce188cb6b
1 in β†’ 1 out12.3500 XPM110 B
AGc7t72t…UnvYxLPB
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.

1.449 Γ— 10⁹⁰(91-digit number)
14496798454403059345…98355885775295720639
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
1.449 Γ— 10⁹⁰(91-digit number)
14496798454403059345…98355885775295720639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.899 Γ— 10⁹⁰(91-digit number)
28993596908806118690…96711771550591441279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.798 Γ— 10⁹⁰(91-digit number)
57987193817612237380…93423543101182882559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.159 Γ— 10⁹¹(92-digit number)
11597438763522447476…86847086202365765119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.319 Γ— 10⁹¹(92-digit number)
23194877527044894952…73694172404731530239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.638 Γ— 10⁹¹(92-digit number)
46389755054089789904…47388344809463060479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.277 Γ— 10⁹¹(92-digit number)
92779510108179579808…94776689618926120959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.855 Γ— 10⁹²(93-digit number)
18555902021635915961…89553379237852241919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.711 Γ— 10⁹²(93-digit number)
37111804043271831923…79106758475704483839
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,723,728 XPMΒ·at block #6,809,956 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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