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Block #48,362

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 3:00:27 PM Β· Difficulty 8.8431 Β· 6,762,321 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4c4d9d9df3ad842a8d0dcfe9194f368fc5584d6ca0f5e9b549ae42d27a71ac15
View on Chainz β†—

Height

#48,362

Difficulty

8.843071

Transactions

2

Size

7.40 KB

Version

2

Bits

08d7d37d

Nonce

195

Timestamp

7/15/2013, 3:00:27 PM

Confirmations

6,762,321

Mined by

⛏️ P2SHAbaRiLS3G88Jm5oARhiZ6VaC8uwZbSr2aA

Merkle Root

1ec7133abcb4d70549b7a5f7e3bd9acdf59f6ab85895d3f75bb2183716195f3b
Transactions (2)
Coinbase43e016d36833f0…e4b36e5f16113f
1 in β†’ 1 out12.8500 XPM110 B
AbaRiLS3…wZbSr2aA
0ef6f61fe0e660…755ec0ffe6500b
64 in β†’ 1 out1000.0000 XPM7.20 KB
AVDE9j9c…DXexEzBD
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.

2.365 Γ— 10⁹⁢(97-digit number)
23652873132467813669…59981437819008345199
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
2.365 Γ— 10⁹⁢(97-digit number)
23652873132467813669…59981437819008345199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.365 Γ— 10⁹⁢(97-digit number)
23652873132467813669…59981437819008345201
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
4.730 Γ— 10⁹⁢(97-digit number)
47305746264935627338…19962875638016690399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.730 Γ— 10⁹⁢(97-digit number)
47305746264935627338…19962875638016690401
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
9.461 Γ— 10⁹⁢(97-digit number)
94611492529871254677…39925751276033380799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.461 Γ— 10⁹⁢(97-digit number)
94611492529871254677…39925751276033380801
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
1.892 Γ— 10⁹⁷(98-digit number)
18922298505974250935…79851502552066761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.892 Γ— 10⁹⁷(98-digit number)
18922298505974250935…79851502552066761601
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
3.784 Γ— 10⁹⁷(98-digit number)
37844597011948501870…59703005104133523199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,729,556 XPMΒ·at block #6,810,682 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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