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Block #1,924,535

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/5/2017, 5:12:22 AM Β· Difficulty 10.7219 Β· 4,918,766 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e3c66e666f888bafe314669f9db544fdc7805b79a93eb4b91568cd1d0ec901d
View on Chainz β†—

Height

#1,924,535

Difficulty

10.721885

Transactions

1

Size

198 B

Version

2

Bits

0ab8cd6e

Nonce

8,357,037

Timestamp

1/5/2017, 5:12:22 AM

Confirmations

4,918,766

Mined by

⛏️ P2SHAeBoWcCg68wJJTxSAyPP5vmWRB46Sgo9PN

Merkle Root

6187baa1c85e72e91e87dc54354bd04cffa784e3d3fddaa61134edea90454f41
Transactions (1)
Coinbase6187baa1c85e72…34edea90454f41
1 in β†’ 1 out8.6900 XPM109 B
AeBoWcCg…46Sgo9PN
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.

3.952 Γ— 10⁹²(93-digit number)
39528459221173308059…99430319019849353839
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
3.952 Γ— 10⁹²(93-digit number)
39528459221173308059…99430319019849353839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.905 Γ— 10⁹²(93-digit number)
79056918442346616119…98860638039698707679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.581 Γ— 10⁹³(94-digit number)
15811383688469323223…97721276079397415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.162 Γ— 10⁹³(94-digit number)
31622767376938646447…95442552158794830719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.324 Γ— 10⁹³(94-digit number)
63245534753877292895…90885104317589661439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁴(95-digit number)
12649106950775458579…81770208635179322879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.529 Γ— 10⁹⁴(95-digit number)
25298213901550917158…63540417270358645759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.059 Γ— 10⁹⁴(95-digit number)
50596427803101834316…27080834540717291519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁡(96-digit number)
10119285560620366863…54161669081434583039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.023 Γ— 10⁹⁡(96-digit number)
20238571121240733726…08323338162869166079
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:57,990,773 XPMΒ·at block #6,843,300 Β· updates every 60s
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