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Block #217,655

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/19/2013, 11:59:31 AM Β· Difficulty 9.9284 Β· 6,585,588 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
041f2f72c783666ec519ebd52f37f92666266775cb8b9f293f5d592e6631d79b
View on Chainz β†—

Height

#217,655

Difficulty

9.928398

Transactions

1

Size

197 B

Version

2

Bits

09edab82

Nonce

159,286

Timestamp

10/19/2013, 11:59:31 AM

Confirmations

6,585,588

Mined by

⛏️ P2SHARBvr1evuYzdjmXQBMTxCmA4hCNg7YPkPH

Merkle Root

a36f4371e4c2b989dd80bf912d22d77881cf1297a72675899961c951b3b199d9
Transactions (1)
Coinbasea36f4371e4c2b9…61c951b3b199d9
1 in β†’ 1 out10.1300 XPM109 B
ARBvr1ev…Ng7YPkPH
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.

8.560 Γ— 10⁹⁰(91-digit number)
85603188482142152240…76009799959578926159
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
8.560 Γ— 10⁹⁰(91-digit number)
85603188482142152240…76009799959578926159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.712 Γ— 10⁹¹(92-digit number)
17120637696428430448…52019599919157852319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.424 Γ— 10⁹¹(92-digit number)
34241275392856860896…04039199838315704639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.848 Γ— 10⁹¹(92-digit number)
68482550785713721792…08078399676631409279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.369 Γ— 10⁹²(93-digit number)
13696510157142744358…16156799353262818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.739 Γ— 10⁹²(93-digit number)
27393020314285488717…32313598706525637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.478 Γ— 10⁹²(93-digit number)
54786040628570977434…64627197413051274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.095 Γ— 10⁹³(94-digit number)
10957208125714195486…29254394826102548479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.191 Γ— 10⁹³(94-digit number)
21914416251428390973…58508789652205096959
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:57,669,972 XPMΒ·at block #6,803,242 Β· updates every 60s
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