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Block #1,534,491

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 6:50:30 AM Β· Difficulty 10.6174 Β· 5,292,671 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
efac9580239e18cdabfb393689ccbf66291f7ba1bbd606892bb4727c8b476fae
View on Chainz β†—

Height

#1,534,491

Difficulty

10.617406

Transactions

3

Size

15.02 KB

Version

2

Bits

0a9e0e56

Nonce

269,521,706

Timestamp

4/10/2016, 6:50:30 AM

Confirmations

5,292,671

Mined by

⛏️ P2SHAcV7Q4jVkz2pnCKxptGXEEMmRL8APXPeFX

Merkle Root

b6cd99326a5a2d440666f712c1bf89dce8fc59eb1f4022fc3864333316cd6c60
Transactions (3)
Coinbase0f42b0274473d7…ac652c20daa65c
1 in β†’ 1 out9.0200 XPM109 B
AcV7Q4jV…8APXPeFX
dd35956cb16886…bad7eb02bdbd15
51 in β†’ 1 out550.8422 XPM7.42 KB
AckENN7U…uxjU121w
56064abfaa80d9…792e2f5dc0ec0d
51 in β†’ 1 out2756.3100 XPM7.41 KB
AY6fjrd1…5q6Uxa8g
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.

8.503 Γ— 10⁹⁢(97-digit number)
85036921955163329633…03126928886716661759
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
8.503 Γ— 10⁹⁢(97-digit number)
85036921955163329633…03126928886716661759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.700 Γ— 10⁹⁷(98-digit number)
17007384391032665926…06253857773433323519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.401 Γ— 10⁹⁷(98-digit number)
34014768782065331853…12507715546866647039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.802 Γ— 10⁹⁷(98-digit number)
68029537564130663706…25015431093733294079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.360 Γ— 10⁹⁸(99-digit number)
13605907512826132741…50030862187466588159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.721 Γ— 10⁹⁸(99-digit number)
27211815025652265482…00061724374933176319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.442 Γ— 10⁹⁸(99-digit number)
54423630051304530965…00123448749866352639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁹(100-digit number)
10884726010260906193…00246897499732705279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.176 Γ— 10⁹⁹(100-digit number)
21769452020521812386…00493794999465410559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.353 Γ— 10⁹⁹(100-digit number)
43538904041043624772…00987589998930821119
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:57,861,481 XPMΒ·at block #6,827,161 Β· updates every 60s
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