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Block #3,140,704

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/15/2019, 5:46:25 PM Β· Difficulty 11.3131 Β· 3,697,712 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b3e295c6afc7bb6844c2e15a09ed01effd5c3dabd35a867a22149c8fc4b68d7c
View on Chainz β†—

Height

#3,140,704

Difficulty

11.313092

Transactions

2

Size

574 B

Version

2

Bits

0b5026d3

Nonce

896,242,144

Timestamp

4/15/2019, 5:46:25 PM

Confirmations

3,697,712

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

61b08699cab8721a7a20d3b46a3f051310983a4675d6bc23335b95965981865a
Transactions (2)
Coinbase052cd4e0d0574e…5a52f533f87464
1 in β†’ 1 out7.8100 XPM110 B
AbXwmGxD…4XXYP765
b2331af288b118…02c17f333dd2c2
2 in β†’ 2 out275.5761 XPM374 B
AeTHTL7A…vT1872bkAVzY8wER…FqpmF5rd
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.

5.066 Γ— 10⁹³(94-digit number)
50668369750381385043…02052502494305179939
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
5.066 Γ— 10⁹³(94-digit number)
50668369750381385043…02052502494305179939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.013 Γ— 10⁹⁴(95-digit number)
10133673950076277008…04105004988610359879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.026 Γ— 10⁹⁴(95-digit number)
20267347900152554017…08210009977220719759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.053 Γ— 10⁹⁴(95-digit number)
40534695800305108035…16420019954441439519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.106 Γ— 10⁹⁴(95-digit number)
81069391600610216070…32840039908882879039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.621 Γ— 10⁹⁡(96-digit number)
16213878320122043214…65680079817765758079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.242 Γ— 10⁹⁡(96-digit number)
32427756640244086428…31360159635531516159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.485 Γ— 10⁹⁡(96-digit number)
64855513280488172856…62720319271063032319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.297 Γ— 10⁹⁢(97-digit number)
12971102656097634571…25440638542126064639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.594 Γ— 10⁹⁢(97-digit number)
25942205312195269142…50881277084252129279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.188 Γ— 10⁹⁢(97-digit number)
51884410624390538284…01762554168504258559
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:57,951,601 XPMΒ·at block #6,838,415 Β· updates every 60s
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