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Block #2,751,548

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2018, 3:40:04 PM Β· Difficulty 11.6429 Β· 4,085,235 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5e86d6d34b6748a5acdb952f2c82b904c96d8f65b3eb75502fc9844d05b0c050
View on Chainz β†—

Height

#2,751,548

Difficulty

11.642925

Transactions

2

Size

724 B

Version

2

Bits

0ba496be

Nonce

721,984,917

Timestamp

7/16/2018, 3:40:04 PM

Confirmations

4,085,235

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

3f8de6f8d6b5bfe4b6e2173d8f57c7d50484d7f9d60527dfcb32f0082dcd6aae
Transactions (2)
Coinbase590213ad2b0517…f3dbaf42ea0071
1 in β†’ 1 out7.3700 XPM110 B
AZtxQr2F…7grUWrUz
d14a2f1e2d5eaf…8efc8990244923
3 in β†’ 2 out10.0100 XPM523 B
AWTAGcL4…jKZwu5r5AXXHoC9j…8o8n25h6
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.

2.499 Γ— 10⁹⁢(97-digit number)
24995601765828732174…91270145226196796479
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
2.499 Γ— 10⁹⁢(97-digit number)
24995601765828732174…91270145226196796479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.999 Γ— 10⁹⁢(97-digit number)
49991203531657464349…82540290452393592959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.998 Γ— 10⁹⁢(97-digit number)
99982407063314928698…65080580904787185919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.999 Γ— 10⁹⁷(98-digit number)
19996481412662985739…30161161809574371839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.999 Γ— 10⁹⁷(98-digit number)
39992962825325971479…60322323619148743679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.998 Γ— 10⁹⁷(98-digit number)
79985925650651942958…20644647238297487359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.599 Γ— 10⁹⁸(99-digit number)
15997185130130388591…41289294476594974719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.199 Γ— 10⁹⁸(99-digit number)
31994370260260777183…82578588953189949439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.398 Γ— 10⁹⁸(99-digit number)
63988740520521554366…65157177906379898879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.279 Γ— 10⁹⁹(100-digit number)
12797748104104310873…30314355812759797759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.559 Γ— 10⁹⁹(100-digit number)
25595496208208621746…60628711625519595519
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:57,938,543 XPMΒ·at block #6,836,782 Β· updates every 60s
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