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Block #2,096,347

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2017, 10:44:21 PM Β· Difficulty 10.8719 Β· 4,728,545 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d9e3ac144f6c0dd93a0afeaeb786b8dd6acf31da0b13ccb8a73808a25662c9c
View on Chainz β†—

Height

#2,096,347

Difficulty

10.871863

Transactions

2

Size

1.58 KB

Version

2

Bits

0adf3268

Nonce

652,475,639

Timestamp

5/1/2017, 10:44:21 PM

Confirmations

4,728,545

Mined by

⛏️ P2SHAXAYAVERHkPnwMDF42vH9ZEwjF9q8fyKna

Merkle Root

f33c5d0a1b576e58e7b71c2e3272fe3d587845d538a6771f528bdbe9d24fb27b
Transactions (2)
Coinbase449c4e68811d43…62f300608addef
1 in β†’ 1 out8.4700 XPM110 B
AXAYAVER…9q8fyKna
d73dcfdb3812c1…3390234bca9551
9 in β†’ 2 out4.9982 XPM1.38 KB
AKGxoSP8…8oH3hVLdAU4cKHhq…bgx1Gzz9
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.

4.353 Γ— 10⁹³(94-digit number)
43535848486622156391…33735265630337099489
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
4.353 Γ— 10⁹³(94-digit number)
43535848486622156391…33735265630337099489
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.707 Γ— 10⁹³(94-digit number)
87071696973244312782…67470531260674198979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁴(95-digit number)
17414339394648862556…34941062521348397959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.482 Γ— 10⁹⁴(95-digit number)
34828678789297725112…69882125042696795919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.965 Γ— 10⁹⁴(95-digit number)
69657357578595450225…39764250085393591839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁡(96-digit number)
13931471515719090045…79528500170787183679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.786 Γ— 10⁹⁡(96-digit number)
27862943031438180090…59057000341574367359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.572 Γ— 10⁹⁡(96-digit number)
55725886062876360180…18114000683148734719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁢(97-digit number)
11145177212575272036…36228001366297469439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.229 Γ— 10⁹⁢(97-digit number)
22290354425150544072…72456002732594938879
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:57,843,217 XPMΒ·at block #6,824,891 Β· updates every 60s
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