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Block #1,611,493

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2016, 9:29:50 PM Β· Difficulty 10.6057 Β· 5,230,851 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
38193b6c1a538dc075dcbb00da5e10d8c7cf0a9fd4fb7c85da8ae2205075f133
View on Chainz β†—

Height

#1,611,493

Difficulty

10.605703

Transactions

1

Size

199 B

Version

2

Bits

0a9b0f53

Nonce

902,065,904

Timestamp

6/2/2016, 9:29:50 PM

Confirmations

5,230,851

Mined by

⛏️ P2SHATyrwB5i8SLgxpeojPEt3TTLSo6JzvwXFt

Merkle Root

1dfe38d785de1e52a43992b30fd24fc6b94d3ccdb899b883ae05aad01c54f042
Transactions (1)
Coinbase1dfe38d785de1e…05aad01c54f042
1 in β†’ 1 out8.8800 XPM109 B
ATyrwB5i…6JzvwXFt
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.

2.350 Γ— 10⁹⁡(96-digit number)
23507659118479685033…91649055743327406079
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
2.350 Γ— 10⁹⁡(96-digit number)
23507659118479685033…91649055743327406079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.701 Γ— 10⁹⁡(96-digit number)
47015318236959370067…83298111486654812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.403 Γ— 10⁹⁡(96-digit number)
94030636473918740135…66596222973309624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.880 Γ— 10⁹⁢(97-digit number)
18806127294783748027…33192445946619248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.761 Γ— 10⁹⁢(97-digit number)
37612254589567496054…66384891893238497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.522 Γ— 10⁹⁢(97-digit number)
75224509179134992108…32769783786476994559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.504 Γ— 10⁹⁷(98-digit number)
15044901835826998421…65539567572953989119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.008 Γ— 10⁹⁷(98-digit number)
30089803671653996843…31079135145907978239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.017 Γ— 10⁹⁷(98-digit number)
60179607343307993686…62158270291815956479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁸(99-digit number)
12035921468661598737…24316540583631912959
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:57,983,159 XPMΒ·at block #6,842,343 Β· updates every 60s
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