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Block #149,049

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 2:51:52 AM Β· Difficulty 9.8568 Β· 6,662,003 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7e2ebe2617803d5278bdea6b2328b176bf3518f58c83c1d3e039b901f4c03a00
View on Chainz β†—

Height

#149,049

Difficulty

9.856843

Transactions

1

Size

198 B

Version

2

Bits

09db5a0e

Nonce

168,081

Timestamp

9/4/2013, 2:51:52 AM

Confirmations

6,662,003

Mined by

⛏️ P2SHAM9R37qPciuhUNYvwcMUHTUsnwhm8dCX8m

Merkle Root

379a2c7ac2c7c88ff915deaeafd961a858883d4c05a3e5315c0436c26ccade59
Transactions (1)
Coinbase379a2c7ac2c7c8…0436c26ccade59
1 in β†’ 1 out10.2800 XPM109 B
AM9R37qP…hm8dCX8m
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.

1.040 Γ— 10⁹²(93-digit number)
10406860295780796862…54080369553027568639
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
1.040 Γ— 10⁹²(93-digit number)
10406860295780796862…54080369553027568639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.081 Γ— 10⁹²(93-digit number)
20813720591561593725…08160739106055137279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.162 Γ— 10⁹²(93-digit number)
41627441183123187451…16321478212110274559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.325 Γ— 10⁹²(93-digit number)
83254882366246374903…32642956424220549119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.665 Γ— 10⁹³(94-digit number)
16650976473249274980…65285912848441098239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.330 Γ— 10⁹³(94-digit number)
33301952946498549961…30571825696882196479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.660 Γ— 10⁹³(94-digit number)
66603905892997099922…61143651393764392959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.332 Γ— 10⁹⁴(95-digit number)
13320781178599419984…22287302787528785919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.664 Γ— 10⁹⁴(95-digit number)
26641562357198839969…44574605575057571839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,732,528 XPMΒ·at block #6,811,051 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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