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Block #1,970,927

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/6/2017, 12:41:35 AM Β· Difficulty 10.7541 Β· 4,873,696 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
11616e6d5e2aac69b16d818d0ac2a019653789af889d587c261e64db274f4362
View on Chainz β†—

Height

#1,970,927

Difficulty

10.754066

Transactions

2

Size

1.86 KB

Version

2

Bits

0ac10a79

Nonce

490,019,462

Timestamp

2/6/2017, 12:41:35 AM

Confirmations

4,873,696

Mined by

⛏️ P2SHAc6q3Le8vFCyDK7gCfn1z5wzLkWKzC2hxs

Merkle Root

263c4856f56ea652bd614e521feccd906fb44ea84d05a046ac6a13b5d030669f
Transactions (2)
Coinbaseecec9a282b6c2e…76ad71d532acce
1 in β†’ 1 out8.6500 XPM109 B
Ac6q3Le8…WKzC2hxs
ad95c76828e8e1…4538a7149ad31d
11 in β†’ 2 out664.3770 XPM1.66 KB
AdKR6a2M…XUWt9DeAAbfHPQRP…cc1QCTYa
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.

1.050 Γ— 10⁹⁡(96-digit number)
10501048331937630208…92745440803596819359
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
1.050 Γ— 10⁹⁡(96-digit number)
10501048331937630208…92745440803596819359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.100 Γ— 10⁹⁡(96-digit number)
21002096663875260417…85490881607193638719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.200 Γ— 10⁹⁡(96-digit number)
42004193327750520835…70981763214387277439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.400 Γ— 10⁹⁡(96-digit number)
84008386655501041670…41963526428774554879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.680 Γ— 10⁹⁢(97-digit number)
16801677331100208334…83927052857549109759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.360 Γ— 10⁹⁢(97-digit number)
33603354662200416668…67854105715098219519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.720 Γ— 10⁹⁢(97-digit number)
67206709324400833336…35708211430196439039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.344 Γ— 10⁹⁷(98-digit number)
13441341864880166667…71416422860392878079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.688 Γ— 10⁹⁷(98-digit number)
26882683729760333334…42832845720785756159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.376 Γ— 10⁹⁷(98-digit number)
53765367459520666668…85665691441571512319
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:58,001,388 XPMΒ·at block #6,844,622 Β· updates every 60s
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