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Block #1,515,919

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/28/2016, 12:46:41 PM Β· Difficulty 10.6000 Β· 5,293,955 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0eb6c7425b073c5b7a171d86d96191dc3f4de08f9a43943f1acf19b488a2dca3
View on Chainz β†—

Height

#1,515,919

Difficulty

10.599973

Transactions

2

Size

69.76 KB

Version

2

Bits

0a9997d6

Nonce

1,103,891,570

Timestamp

3/28/2016, 12:46:41 PM

Confirmations

5,293,955

Mined by

⛏️ P2SHARcDWim9xxshEMeBA3QC8jdspVa1W6L1JB

Merkle Root

49d522dc659328e85f5bd57a20ada5cd8569e2188e62f81db6c9bbfeef33b0e7
Transactions (2)
Coinbase5c304a21a3c766…2f3ad0c8a2ab7a
1 in β†’ 1 out9.6100 XPM109 B
ARcDWim9…a1W6L1JB
4687d0bc994e6b…b66960d26c1957
481 in β†’ 1 out8.0000 XPM69.56 KB
AW9z6iyE…ZMok5rfx
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.

1.451 Γ— 10⁹²(93-digit number)
14518369387497186710…39964046002745824399
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
1.451 Γ— 10⁹²(93-digit number)
14518369387497186710…39964046002745824399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.451 Γ— 10⁹²(93-digit number)
14518369387497186710…39964046002745824401
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
2.903 Γ— 10⁹²(93-digit number)
29036738774994373420…79928092005491648799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.903 Γ— 10⁹²(93-digit number)
29036738774994373420…79928092005491648801
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
5.807 Γ— 10⁹²(93-digit number)
58073477549988746840…59856184010983297599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.807 Γ— 10⁹²(93-digit number)
58073477549988746840…59856184010983297601
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
1.161 Γ— 10⁹³(94-digit number)
11614695509997749368…19712368021966595199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.161 Γ— 10⁹³(94-digit number)
11614695509997749368…19712368021966595201
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
2.322 Γ— 10⁹³(94-digit number)
23229391019995498736…39424736043933190399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.322 Γ— 10⁹³(94-digit number)
23229391019995498736…39424736043933190401
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:57,723,078 XPMΒ·at block #6,809,873 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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