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Block #919,939

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/2/2015, 2:10:12 PM Β· Difficulty 10.9191 Β· 5,887,905 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
731c7b5b33e5208dfddb0b7c131f1826c41065b020638159caaf2c54065ab086
View on Chainz β†—

Height

#919,939

Difficulty

10.919107

Transactions

2

Size

5.48 KB

Version

2

Bits

0aeb4a9d

Nonce

84,947,495

Timestamp

2/2/2015, 2:10:12 PM

Confirmations

5,887,905

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b96d362c657bece8501a9f7743a5b476da9977d9810d9d8f6321bb961701ac04
Transactions (2)
Coinbasebc0f77a7cefaa7…14be37a6c6c675
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
fec61df99d0a23…bebd6fbe2ad435
36 in β†’ 2 out1637.8394 XPM5.28 KB
AXAcd8xZ…JcB365TpAQdwGrbc…JF8HxK6k
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.

7.173 Γ— 10⁹⁢(97-digit number)
71737641773879905737…60693698969755487999
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
7.173 Γ— 10⁹⁢(97-digit number)
71737641773879905737…60693698969755487999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.173 Γ— 10⁹⁢(97-digit number)
71737641773879905737…60693698969755488001
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
1.434 Γ— 10⁹⁷(98-digit number)
14347528354775981147…21387397939510975999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.434 Γ— 10⁹⁷(98-digit number)
14347528354775981147…21387397939510976001
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
2.869 Γ— 10⁹⁷(98-digit number)
28695056709551962294…42774795879021951999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.869 Γ— 10⁹⁷(98-digit number)
28695056709551962294…42774795879021952001
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
5.739 Γ— 10⁹⁷(98-digit number)
57390113419103924589…85549591758043903999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.739 Γ— 10⁹⁷(98-digit number)
57390113419103924589…85549591758043904001
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
1.147 Γ— 10⁹⁸(99-digit number)
11478022683820784917…71099183516087807999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.147 Γ— 10⁹⁸(99-digit number)
11478022683820784917…71099183516087808001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.295 Γ— 10⁹⁸(99-digit number)
22956045367641569835…42198367032175615999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,706,790 XPMΒ·at block #6,807,843 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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