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Block #207,058

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 5:23:12 AM Β· Difficulty 9.9017 Β· 6,599,573 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
102d4a083002085e18dc90844e92429a23b09882ecc052310fd40b4dfc73a71c
View on Chainz β†—

Height

#207,058

Difficulty

9.901708

Transactions

1

Size

201 B

Version

2

Bits

09e6d64e

Nonce

245,577

Timestamp

10/13/2013, 5:23:12 AM

Confirmations

6,599,573

Mined by

⛏️ P2SHAGD4ELPmV9VxECkLLRQiFxvMNQsYtybN6f

Merkle Root

38183a121f7b185d773b7d1a867dc5d5576871cf833d82e8a903f1176b156b83
Transactions (1)
Coinbase38183a121f7b18…03f1176b156b83
1 in β†’ 1 out10.1800 XPM109 B
AGD4ELPm…sYtybN6f
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.

2.281 Γ— 10⁹⁸(99-digit number)
22819701110936172920…46522283807512094719
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
2.281 Γ— 10⁹⁸(99-digit number)
22819701110936172920…46522283807512094719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.563 Γ— 10⁹⁸(99-digit number)
45639402221872345840…93044567615024189439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.127 Γ— 10⁹⁸(99-digit number)
91278804443744691681…86089135230048378879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.825 Γ— 10⁹⁹(100-digit number)
18255760888748938336…72178270460096757759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.651 Γ— 10⁹⁹(100-digit number)
36511521777497876672…44356540920193515519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.302 Γ— 10⁹⁹(100-digit number)
73023043554995753345…88713081840387031039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.460 Γ— 10¹⁰⁰(101-digit number)
14604608710999150669…77426163680774062079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.920 Γ— 10¹⁰⁰(101-digit number)
29209217421998301338…54852327361548124159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.841 Γ— 10¹⁰⁰(101-digit number)
58418434843996602676…09704654723096248319
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:57,697,148 XPMΒ·at block #6,806,630 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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