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Block #1,937,619

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2017, 4:02:45 PM Β· Difficulty 10.7686 Β· 4,899,301 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8771a289958a4fa6988a150f744c37fd16e8a0ae96bdb4ebf542553995ce875c
View on Chainz β†—

Height

#1,937,619

Difficulty

10.768556

Transactions

2

Size

1.57 KB

Version

2

Bits

0ac4c013

Nonce

1,556,107,115

Timestamp

1/13/2017, 4:02:45 PM

Confirmations

4,899,301

Mined by

⛏️ P2SHALusttX7wq94akZbCqB4grpabyeXYANkjb

Merkle Root

910b204054f143d3ef901a0a8dcd515e7698a63a4ab3eaade195cddfc75cd6ed
Transactions (2)
Coinbasec19f83db210218…a6f869c63750b2
1 in β†’ 1 out8.6300 XPM109 B
ALusttX7…eXYANkjb
8779a7f2a15e68…552a275e868e15
9 in β†’ 2 out28.0100 XPM1.38 KB
AUwo1vZj…93qAT7rYAWDHG5YB…SGfmMSyP
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.

1.679 Γ— 10⁹⁡(96-digit number)
16794083611835464985…09775679898052956959
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
1.679 Γ— 10⁹⁡(96-digit number)
16794083611835464985…09775679898052956959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.358 Γ— 10⁹⁡(96-digit number)
33588167223670929970…19551359796105913919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.717 Γ— 10⁹⁡(96-digit number)
67176334447341859940…39102719592211827839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁢(97-digit number)
13435266889468371988…78205439184423655679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.687 Γ— 10⁹⁢(97-digit number)
26870533778936743976…56410878368847311359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.374 Γ— 10⁹⁢(97-digit number)
53741067557873487952…12821756737694622719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁷(98-digit number)
10748213511574697590…25643513475389245439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁷(98-digit number)
21496427023149395180…51287026950778490879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.299 Γ— 10⁹⁷(98-digit number)
42992854046298790361…02574053901556981759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.598 Γ— 10⁹⁷(98-digit number)
85985708092597580723…05148107803113963519
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:57,939,655 XPMΒ·at block #6,836,919 Β· updates every 60s
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