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Block #2,207,641

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2017, 9:35:54 AM Β· Difficulty 10.9454 Β· 4,631,498 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f84023f375f868377df3a2449ead9657cb1f87e0f905a58c5694ec1ffb5a6a49
View on Chainz β†—

Height

#2,207,641

Difficulty

10.945393

Transactions

2

Size

425 B

Version

2

Bits

0af20545

Nonce

909,320,533

Timestamp

7/15/2017, 9:35:54 AM

Confirmations

4,631,498

Mined by

⛏️ P2SHAe7htxKxd49WEvYRfJzV3W48LBLFYKsWJC

Merkle Root

9f36f23a47fad88d5c0ad110e88ac80fadc9e33b9725172de4586327826a521c
Transactions (2)
Coinbase16955c8f769d5c…110d7447771f90
1 in β†’ 1 out8.3400 XPM110 B
Ae7htxKx…LFYKsWJC
b43d3096b9e745…ef3e32cd246f92
1 in β†’ 2 out21142.8785 XPM225 B
ASag1x3j…mP8y24xbAMNqyy2W…ise9w8w1
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.

1.111 Γ— 10⁹⁴(95-digit number)
11112995527904451498…07199641203774312219
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
1.111 Γ— 10⁹⁴(95-digit number)
11112995527904451498…07199641203774312219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.222 Γ— 10⁹⁴(95-digit number)
22225991055808902996…14399282407548624439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.445 Γ— 10⁹⁴(95-digit number)
44451982111617805992…28798564815097248879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.890 Γ— 10⁹⁴(95-digit number)
88903964223235611984…57597129630194497759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁡(96-digit number)
17780792844647122396…15194259260388995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.556 Γ— 10⁹⁡(96-digit number)
35561585689294244793…30388518520777991039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.112 Γ— 10⁹⁡(96-digit number)
71123171378588489587…60777037041555982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.422 Γ— 10⁹⁢(97-digit number)
14224634275717697917…21554074083111964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.844 Γ— 10⁹⁢(97-digit number)
28449268551435395834…43108148166223928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.689 Γ— 10⁹⁢(97-digit number)
56898537102870791669…86216296332447856639
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:57,957,391 XPMΒ·at block #6,839,138 Β· updates every 60s
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