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Block #155,892

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2013, 3:09:16 PM Β· Difficulty 9.8666 Β· 6,654,444 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5153ff721ee45260235fd83670116701608720f7ad7c85d210574bf35170dc56
View on Chainz β†—

Height

#155,892

Difficulty

9.866582

Transactions

2

Size

980 B

Version

2

Bits

09ddd857

Nonce

21,719

Timestamp

9/8/2013, 3:09:16 PM

Confirmations

6,654,444

Mined by

⛏️ P2SHAbB3iyfpG81PRqK8LeT5oqng7LvApgHS2G

Merkle Root

a9bf47ce1f467e87f7df865055260c55dbab461a67bcc52bccdc5b224f01da30
Transactions (2)
Coinbasedfc4c570628222…1192c5bebdde3c
1 in β†’ 1 out10.2700 XPM109 B
AbB3iyfp…vApgHS2G
e78b7900b3fbb0…036eb24fb8fa6c
5 in β†’ 1 out10.0933 XPM783 B
Ac6AHy6P…obQfLyE8
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.

1.563 Γ— 10⁸⁹(90-digit number)
15639044744654931093…70839710094271517919
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
1.563 Γ— 10⁸⁹(90-digit number)
15639044744654931093…70839710094271517919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.563 Γ— 10⁸⁹(90-digit number)
15639044744654931093…70839710094271517921
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
3.127 Γ— 10⁸⁹(90-digit number)
31278089489309862186…41679420188543035839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.127 Γ— 10⁸⁹(90-digit number)
31278089489309862186…41679420188543035841
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
6.255 Γ— 10⁸⁹(90-digit number)
62556178978619724372…83358840377086071679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.255 Γ— 10⁸⁹(90-digit number)
62556178978619724372…83358840377086071681
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
1.251 Γ— 10⁹⁰(91-digit number)
12511235795723944874…66717680754172143359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.251 Γ— 10⁹⁰(91-digit number)
12511235795723944874…66717680754172143361
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
2.502 Γ— 10⁹⁰(91-digit number)
25022471591447889748…33435361508344286719
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:57,726,769 XPMΒ·at block #6,810,335 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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