XPM Prime Explorer symbol
XPMPrime Explorer

Block #83,907

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2013, 11:24:22 AM Β· Difficulty 9.2707 Β· 6,725,823 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d484eb1270ef0f1ff13ae6fd13dbd6cd20ffb3c9f30ea7dde541f19880e4deb7
View on Chainz β†—

Height

#83,907

Difficulty

9.270653

Transactions

1

Size

201 B

Version

2

Bits

09454984

Nonce

347,708

Timestamp

7/26/2013, 11:24:22 AM

Confirmations

6,725,823

Mined by

⛏️ P2SHAc3AUHowoddp8FyKEjyx2vqHMdhYeSm7Mw

Merkle Root

fa84fbffb41dce0ed6e47aa4b3318edaff869ba3effccca4af7506fa3bda1071
Transactions (1)
Coinbasefa84fbffb41dce…7506fa3bda1071
1 in β†’ 1 out11.6200 XPM109 B
Ac3AUHow…hYeSm7Mw
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.

1.198 Γ— 10¹⁰⁰(101-digit number)
11981808906028744668…02303389611177356809
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
1.198 Γ— 10¹⁰⁰(101-digit number)
11981808906028744668…02303389611177356809
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.198 Γ— 10¹⁰⁰(101-digit number)
11981808906028744668…02303389611177356811
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
2.396 Γ— 10¹⁰⁰(101-digit number)
23963617812057489336…04606779222354713619
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.396 Γ— 10¹⁰⁰(101-digit number)
23963617812057489336…04606779222354713621
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
4.792 Γ— 10¹⁰⁰(101-digit number)
47927235624114978673…09213558444709427239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.792 Γ— 10¹⁰⁰(101-digit number)
47927235624114978673…09213558444709427241
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
9.585 Γ— 10¹⁰⁰(101-digit number)
95854471248229957346…18427116889418854479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.585 Γ— 10¹⁰⁰(101-digit number)
95854471248229957346…18427116889418854481
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
1.917 Γ— 10¹⁰¹(102-digit number)
19170894249645991469…36854233778837708959
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:57,721,922 XPMΒ·at block #6,809,729 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