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Block #749,691

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/2/2014, 11:08:44 AM Β· Difficulty 10.9761 Β· 6,076,453 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d33629813b6bc706309eb89e40289d41d21d45618f5ec1a5af9656eeedaa5ad9
View on Chainz β†—

Height

#749,691

Difficulty

10.976114

Transactions

2

Size

11.66 KB

Version

2

Bits

0af9e295

Nonce

69,969,878

Timestamp

10/2/2014, 11:08:44 AM

Confirmations

6,076,453

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

65f6ed434b88791f608f533679e97f50218f43e18e4b9c3560ad9e52742705dc
Transactions (2)
Coinbaseaaf6e8fcec4f36…89baf1cb779780
1 in β†’ 1 out8.4196 XPM116 B
ANSXnLY2…Sd25TjkD
a07de95bec67fd…5993b2448f7195
79 in β†’ 1 out13.3700 XPM11.45 KB
AH5UMhMN…Vs3PwKK8
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.

3.375 Γ— 10⁹⁢(97-digit number)
33754197953046977972…80345689405104435199
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
3.375 Γ— 10⁹⁢(97-digit number)
33754197953046977972…80345689405104435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.750 Γ— 10⁹⁢(97-digit number)
67508395906093955944…60691378810208870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.350 Γ— 10⁹⁷(98-digit number)
13501679181218791188…21382757620417740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.700 Γ— 10⁹⁷(98-digit number)
27003358362437582377…42765515240835481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.400 Γ— 10⁹⁷(98-digit number)
54006716724875164755…85531030481670963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁸(99-digit number)
10801343344975032951…71062060963341926399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.160 Γ— 10⁹⁸(99-digit number)
21602686689950065902…42124121926683852799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.320 Γ— 10⁹⁸(99-digit number)
43205373379900131804…84248243853367705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.641 Γ— 10⁹⁸(99-digit number)
86410746759800263608…68496487706735411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁹(100-digit number)
17282149351960052721…36992975413470822399
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:57,853,277 XPMΒ·at block #6,826,143 Β· updates every 60s
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