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Block #3,170,509

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2019, 10:45:22 AM Β· Difficulty 11.3120 Β· 3,671,848 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
34e9e60690886c0965e4a01c45b5941bbcba37116d3d41eefe505ac0cd136b48
View on Chainz β†—

Height

#3,170,509

Difficulty

11.312045

Transactions

2

Size

11.83 KB

Version

2

Bits

0b4fe231

Nonce

1,773,521,319

Timestamp

5/6/2019, 10:45:22 AM

Confirmations

3,671,848

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

01b09eab64f729501b1caa11ed4ced63f2b0c5e0437550d4066d3044bdb95c81
Transactions (2)
Coinbase0a6094bfb169cc…e4ba78f22fdb8a
1 in β†’ 1 out7.9900 XPM110 B
AbXwmGxD…4XXYP765
e3bf325559c050…76a5b58b3cc76a
80 in β†’ 2 out2369.6293 XPM11.63 KB
AUkreMvG…b7xaeFPaAPQ9gg1V…H4v8MyZ4
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.

9.189 Γ— 10⁹⁡(96-digit number)
91894272164937165306…23279901186573169279
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
9.189 Γ— 10⁹⁡(96-digit number)
91894272164937165306…23279901186573169279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.837 Γ— 10⁹⁢(97-digit number)
18378854432987433061…46559802373146338559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.675 Γ— 10⁹⁢(97-digit number)
36757708865974866122…93119604746292677119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.351 Γ— 10⁹⁢(97-digit number)
73515417731949732244…86239209492585354239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.470 Γ— 10⁹⁷(98-digit number)
14703083546389946448…72478418985170708479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.940 Γ— 10⁹⁷(98-digit number)
29406167092779892897…44956837970341416959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.881 Γ— 10⁹⁷(98-digit number)
58812334185559785795…89913675940682833919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁸(99-digit number)
11762466837111957159…79827351881365667839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.352 Γ— 10⁹⁸(99-digit number)
23524933674223914318…59654703762731335679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.704 Γ— 10⁹⁸(99-digit number)
47049867348447828636…19309407525462671359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.409 Γ— 10⁹⁸(99-digit number)
94099734696895657273…38618815050925342719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,983,263 XPMΒ·at block #6,842,356 Β· updates every 60s
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