XPM Prime Explorer symbol
XPMPrime Explorer

Block #54,237

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 7:23:30 PM Β· Difficulty 8.9315 Β· 6,752,385 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
14e46af6c78c2a0d97b4a5e94ff078fc54f25b0de3a75c9757b3a59b6ea4d840
View on Chainz β†—

Height

#54,237

Difficulty

8.931541

Transactions

1

Size

198 B

Version

2

Bits

08ee7974

Nonce

136

Timestamp

7/16/2013, 7:23:30 PM

Confirmations

6,752,385

Mined by

⛏️ P2SHALtQiCynzfouqbRxJ6ViGNCLqY68VU6xPK

Merkle Root

a6f8fc6dc9ca8ce724f46da5cd0b2f45d3c66def348e8561f90569f710ded54c
Transactions (1)
Coinbasea6f8fc6dc9ca8c…0569f710ded54c
1 in β†’ 1 out12.5200 XPM110 B
ALtQiCyn…68VU6xPK
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.

2.406 Γ— 10⁹⁰(91-digit number)
24064107168338074547…46006197526487507589
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
2.406 Γ— 10⁹⁰(91-digit number)
24064107168338074547…46006197526487507589
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.406 Γ— 10⁹⁰(91-digit number)
24064107168338074547…46006197526487507591
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
4.812 Γ— 10⁹⁰(91-digit number)
48128214336676149094…92012395052975015179
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.812 Γ— 10⁹⁰(91-digit number)
48128214336676149094…92012395052975015181
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
9.625 Γ— 10⁹⁰(91-digit number)
96256428673352298188…84024790105950030359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.625 Γ— 10⁹⁰(91-digit number)
96256428673352298188…84024790105950030361
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
1.925 Γ— 10⁹¹(92-digit number)
19251285734670459637…68049580211900060719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.925 Γ— 10⁹¹(92-digit number)
19251285734670459637…68049580211900060721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,697,077 XPMΒ·at block #6,806,621 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy