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Block #733,450

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/21/2014, 12:47:20 PM Β· Difficulty 10.9730 Β· 6,076,281 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
762c0dc7b8fb6b74c17dddbbce6e21bec1a738c3726aa14b391b1e317e327203
View on Chainz β†—

Height

#733,450

Difficulty

10.973021

Transactions

2

Size

1.14 KB

Version

2

Bits

0af917ef

Nonce

1,130,196,214

Timestamp

9/21/2014, 12:47:20 PM

Confirmations

6,076,281

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ca017e7eb3a5ac67b9412e82f8c844cb641b94b652c4a1b994c57a8816a97c4c
Transactions (2)
Coinbase3ca1d5278bac51…b0e16410cc0bd8
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
38023ade4799ca…726b6f3b920db4
6 in β†’ 2 out78.8598 XPM965 B
AJ9nhVGf…9thQjU4CANN9xPwV…a95rY66K
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.

3.675 Γ— 10⁹⁡(96-digit number)
36753995109150334539…62452542100013733919
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
3.675 Γ— 10⁹⁡(96-digit number)
36753995109150334539…62452542100013733919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.350 Γ— 10⁹⁡(96-digit number)
73507990218300669079…24905084200027467839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.470 Γ— 10⁹⁢(97-digit number)
14701598043660133815…49810168400054935679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.940 Γ— 10⁹⁢(97-digit number)
29403196087320267631…99620336800109871359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.880 Γ— 10⁹⁢(97-digit number)
58806392174640535263…99240673600219742719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁷(98-digit number)
11761278434928107052…98481347200439485439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.352 Γ— 10⁹⁷(98-digit number)
23522556869856214105…96962694400878970879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.704 Γ— 10⁹⁷(98-digit number)
47045113739712428211…93925388801757941759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.409 Γ— 10⁹⁷(98-digit number)
94090227479424856422…87850777603515883519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.881 Γ— 10⁹⁸(99-digit number)
18818045495884971284…75701555207031767039
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:57,721,930 XPMΒ·at block #6,809,730 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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