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Block #1,534,717

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 10:30:40 AM Β· Difficulty 10.6179 Β· 5,282,066 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
75cd74521142d144ff30338901886e97002d7289665b5bbf7b65fddf5d849647
View on Chainz β†—

Height

#1,534,717

Difficulty

10.617899

Transactions

2

Size

7.62 KB

Version

2

Bits

0a9e2e9e

Nonce

386,734,686

Timestamp

4/10/2016, 10:30:40 AM

Confirmations

5,282,066

Mined by

⛏️ P2SHANVkNzV6zQvA6nWye1jbhpVFLR3g9CvHq2

Merkle Root

8c7eeec7d7a6315fb355bb48d3272c273b2dca84e1d808e3999253c829923126
Transactions (2)
Coinbase069aff5885feec…24b0cc305ad3ca
1 in β†’ 1 out8.9400 XPM109 B
ANVkNzV6…3g9CvHq2
97df9c9183f884…ab38da585090c8
51 in β†’ 1 out3090.5079 XPM7.42 KB
AHkjHx3u…Gns5zxPv
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.

4.892 Γ— 10⁹⁴(95-digit number)
48924690169627519480…41014011278417235999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.892 Γ— 10⁹⁴(95-digit number)
48924690169627519480…41014011278417235999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.892 Γ— 10⁹⁴(95-digit number)
48924690169627519480…41014011278417236001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
9.784 Γ— 10⁹⁴(95-digit number)
97849380339255038960…82028022556834471999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.784 Γ— 10⁹⁴(95-digit number)
97849380339255038960…82028022556834472001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.956 Γ— 10⁹⁡(96-digit number)
19569876067851007792…64056045113668943999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.956 Γ— 10⁹⁡(96-digit number)
19569876067851007792…64056045113668944001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.913 Γ— 10⁹⁡(96-digit number)
39139752135702015584…28112090227337887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.913 Γ— 10⁹⁡(96-digit number)
39139752135702015584…28112090227337888001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
7.827 Γ— 10⁹⁡(96-digit number)
78279504271404031168…56224180454675775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.827 Γ— 10⁹⁡(96-digit number)
78279504271404031168…56224180454675776001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,778,299 XPMΒ·at block #6,816,782 Β· updates every 60s
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