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Block #1,534,664

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 9:47:20 AM Β· Difficulty 10.6172 Β· 5,278,365 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f14268849c3987ff30b7da959f618f7822b29b6bfd34ff19aba391d7da6223ea
View on Chainz β†—

Height

#1,534,664

Difficulty

10.617153

Transactions

3

Size

15.02 KB

Version

2

Bits

0a9dfdc3

Nonce

1,683,798,728

Timestamp

4/10/2016, 9:47:20 AM

Confirmations

5,278,365

Mined by

⛏️ P2SHAadY2GQv8DaA4dxaMhffP4jACj5stNaTax

Merkle Root

a2c390d947ae7483e8f27828c61eb740b631bc5d931a8da8e78fd3f078fdb619
Transactions (3)
Coinbase33413b63ef871a…82948c94d7f3c5
1 in β†’ 1 out9.0200 XPM110 B
AadY2GQv…5stNaTax
1eca08a706bf73…5d5b2a4bdcb385
51 in β†’ 1 out1360.1656 XPM7.41 KB
Aassmsue…6Y84djUD
bcccace30696ca…f6e2d3a25c9bda
51 in β†’ 1 out3033.7954 XPM7.41 KB
ALDnC8Ai…wmndbk5D
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.

2.483 Γ— 10⁹⁴(95-digit number)
24830054533679145802…71951530772419726159
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
2.483 Γ— 10⁹⁴(95-digit number)
24830054533679145802…71951530772419726159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.966 Γ— 10⁹⁴(95-digit number)
49660109067358291605…43903061544839452319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.932 Γ— 10⁹⁴(95-digit number)
99320218134716583210…87806123089678904639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.986 Γ— 10⁹⁡(96-digit number)
19864043626943316642…75612246179357809279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.972 Γ— 10⁹⁡(96-digit number)
39728087253886633284…51224492358715618559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.945 Γ— 10⁹⁡(96-digit number)
79456174507773266568…02448984717431237119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.589 Γ— 10⁹⁢(97-digit number)
15891234901554653313…04897969434862474239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.178 Γ— 10⁹⁢(97-digit number)
31782469803109306627…09795938869724948479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.356 Γ— 10⁹⁢(97-digit number)
63564939606218613254…19591877739449896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.271 Γ— 10⁹⁷(98-digit number)
12712987921243722650…39183755478899793919
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:57,748,274 XPMΒ·at block #6,813,028 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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