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Block #1,371,584

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 2:29:24 PM Β· Difficulty 10.8108 Β· 5,471,312 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1f88b09c719413bb4cfd36707f45c8a8e7d390a090a865c078f4fb8323ae8476
View on Chainz β†—

Height

#1,371,584

Difficulty

10.810816

Transactions

2

Size

721 B

Version

2

Bits

0acf91a5

Nonce

414,950,188

Timestamp

12/16/2015, 2:29:24 PM

Confirmations

5,471,312

Mined by

⛏️ P2SHAW8xtmxhY2TFPThwAgjbeesb9QPH5EtZKV

Merkle Root

d4e623097c3381bcb62a62507511a0beca2a6a11d7c5b5fc20ecfa0c366fc79e
Transactions (2)
Coinbaseed76196914d664…9b3cd44d0b90e8
1 in β†’ 1 out8.5500 XPM109 B
AW8xtmxh…PH5EtZKV
8841ba0e27c112…b8bddbf9499005
3 in β†’ 2 out5.1824 XPM522 B
APkcptG3…R9JkCvJoAaTYBfwx…5GZFYFh3
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.

1.531 Γ— 10⁹⁴(95-digit number)
15318730350603564535…17249238114794167819
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
1.531 Γ— 10⁹⁴(95-digit number)
15318730350603564535…17249238114794167819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.063 Γ— 10⁹⁴(95-digit number)
30637460701207129070…34498476229588335639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.127 Γ— 10⁹⁴(95-digit number)
61274921402414258141…68996952459176671279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.225 Γ— 10⁹⁡(96-digit number)
12254984280482851628…37993904918353342559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.450 Γ— 10⁹⁡(96-digit number)
24509968560965703256…75987809836706685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.901 Γ— 10⁹⁡(96-digit number)
49019937121931406512…51975619673413370239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.803 Γ— 10⁹⁡(96-digit number)
98039874243862813025…03951239346826740479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.960 Γ— 10⁹⁢(97-digit number)
19607974848772562605…07902478693653480959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.921 Γ— 10⁹⁢(97-digit number)
39215949697545125210…15804957387306961919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.843 Γ— 10⁹⁢(97-digit number)
78431899395090250420…31609914774613923839
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:57,987,516 XPMΒ·at block #6,842,895 Β· updates every 60s
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