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Block #1,549,531

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/20/2016, 9:35:42 AM Β· Difficulty 10.6523 Β· 5,267,574 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
daaab1a8cd10dfa53375f68710ea91e78bf3f7473b8d6f1ebd1c5581b8f6a6b9
View on Chainz β†—

Height

#1,549,531

Difficulty

10.652313

Transactions

2

Size

1.42 KB

Version

2

Bits

0aa6fdf6

Nonce

375,438,444

Timestamp

4/20/2016, 9:35:42 AM

Confirmations

5,267,574

Mined by

⛏️ P2SHAcX1CJWxx5svaGjidQuSKjrd8dVc4JLi3L

Merkle Root

4cf3c277134049286622c7e5f95876be0ddd0192d4d36190b60b09bb903758d4
Transactions (2)
Coinbase4bc023abaa1838…946ff5e1d09141
1 in β†’ 1 out8.8200 XPM109 B
AcX1CJWx…Vc4JLi3L
70ffb2ce6812f5…22a52a6c1d55a7
8 in β†’ 2 out0.3293 XPM1.23 KB
AemKJ6Uo…31q1UEVKAT1fzTvg…7VeTbpUB
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.

4.755 Γ— 10⁹⁢(97-digit number)
47558417211393927724…99698810683272806399
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
4.755 Γ— 10⁹⁢(97-digit number)
47558417211393927724…99698810683272806399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.755 Γ— 10⁹⁢(97-digit number)
47558417211393927724…99698810683272806401
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
9.511 Γ— 10⁹⁢(97-digit number)
95116834422787855449…99397621366545612799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.511 Γ— 10⁹⁢(97-digit number)
95116834422787855449…99397621366545612801
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
1.902 Γ— 10⁹⁷(98-digit number)
19023366884557571089…98795242733091225599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.902 Γ— 10⁹⁷(98-digit number)
19023366884557571089…98795242733091225601
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
3.804 Γ— 10⁹⁷(98-digit number)
38046733769115142179…97590485466182451199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.804 Γ— 10⁹⁷(98-digit number)
38046733769115142179…97590485466182451201
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
7.609 Γ— 10⁹⁷(98-digit number)
76093467538230284359…95180970932364902399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.609 Γ— 10⁹⁷(98-digit number)
76093467538230284359…95180970932364902401
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:57,780,879 XPMΒ·at block #6,817,104 Β· updates every 60s
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