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Block #150,650

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 4:27:16 AM Β· Difficulty 9.8588 Β· 6,652,875 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6a32ddb5798f8c6ca9edceaa2d5f2c1f7b682db9c5adf2cbe1e23ce760c8f0c
View on Chainz β†—

Height

#150,650

Difficulty

9.858810

Transactions

3

Size

1.45 KB

Version

2

Bits

09dbdafb

Nonce

154,427

Timestamp

9/5/2013, 4:27:16 AM

Confirmations

6,652,875

Mined by

⛏️ P2SHAdcZsTmngF3w7QDKZk3FhMgHUjW8T9Ht6R

Merkle Root

0f96a67bd4644bdb05fa31bdbff16341714e6a0ea9c85028e1758a73b7996ca8
Transactions (3)
Coinbase7b07a6d2a430f1…67b1b030a96a90
1 in β†’ 1 out10.2900 XPM109 B
AdcZsTmn…W8T9Ht6R
413cd5fbce76b8…15f3b4966f0271
4 in β†’ 2 out3012.0100 XPM670 B
APhT8oZ7…2ErKE6TDAJQ5cVZZ…H3C72Pdx
5f5b07fd218e7b…f25c6a3717e8c1
5 in β†’ 1 out51.4500 XPM614 B
Aa571JXD…1d4PwSHX
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.

1.000 Γ— 10⁸⁹(90-digit number)
10003828425251239059…75531822217232993359
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
1.000 Γ— 10⁸⁹(90-digit number)
10003828425251239059…75531822217232993359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.000 Γ— 10⁸⁹(90-digit number)
20007656850502478119…51063644434465986719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.001 Γ— 10⁸⁹(90-digit number)
40015313701004956239…02127288868931973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.003 Γ— 10⁸⁹(90-digit number)
80030627402009912479…04254577737863946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁰(91-digit number)
16006125480401982495…08509155475727893759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.201 Γ— 10⁹⁰(91-digit number)
32012250960803964991…17018310951455787519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.402 Γ— 10⁹⁰(91-digit number)
64024501921607929983…34036621902911575039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.280 Γ— 10⁹¹(92-digit number)
12804900384321585996…68073243805823150079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.560 Γ— 10⁹¹(92-digit number)
25609800768643171993…36146487611646300159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.121 Γ— 10⁹¹(92-digit number)
51219601537286343986…72292975223292600319
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:57,672,227 XPMΒ·at block #6,803,524 Β· updates every 60s
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