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Block #1,634,026

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/18/2016, 2:12:18 PM Β· Difficulty 10.6011 Β· 5,183,743 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96c6457f25e64c6decf4974175d310610db71faae6071eab8845ebe6d5cce4c9
View on Chainz β†—

Height

#1,634,026

Difficulty

10.601112

Transactions

2

Size

20.22 KB

Version

2

Bits

0a99e276

Nonce

677,551,418

Timestamp

6/18/2016, 2:12:18 PM

Confirmations

5,183,743

Mined by

⛏️ P2SHAej8Kgp6pMxbfcEx5L5yZt4mrCa7JSk7mj

Merkle Root

ed901233f4ce392b466817a480e9369757674ef371de7080c27c9c436c69e415
Transactions (2)
Coinbase13ce83e9288251…e29ae3b1d428a2
1 in β†’ 1 out9.1100 XPM109 B
Aej8Kgp6…a7JSk7mj
f83b0fb11a5cf3…ed89f81bf84da8
138 in β†’ 2 out50.0100 XPM20.03 KB
AesJVMS3…WrAkHdm5AdXo5PLF…M55PtHno
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.

7.359 Γ— 10⁹⁴(95-digit number)
73592269709942375693…55532322481521520479
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
7.359 Γ— 10⁹⁴(95-digit number)
73592269709942375693…55532322481521520479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.471 Γ— 10⁹⁡(96-digit number)
14718453941988475138…11064644963043040959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.943 Γ— 10⁹⁡(96-digit number)
29436907883976950277…22129289926086081919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.887 Γ— 10⁹⁡(96-digit number)
58873815767953900554…44258579852172163839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.177 Γ— 10⁹⁢(97-digit number)
11774763153590780110…88517159704344327679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.354 Γ— 10⁹⁢(97-digit number)
23549526307181560221…77034319408688655359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.709 Γ— 10⁹⁢(97-digit number)
47099052614363120443…54068638817377310719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.419 Γ— 10⁹⁢(97-digit number)
94198105228726240887…08137277634754621439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.883 Γ— 10⁹⁷(98-digit number)
18839621045745248177…16274555269509242879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.767 Γ— 10⁹⁷(98-digit number)
37679242091490496354…32549110539018485759
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:57,786,209 XPMΒ·at block #6,817,768 Β· updates every 60s
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