XPM Prime Explorer symbol
XPMPrime Explorer

Block #142,505

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2013, 12:18:56 AM Β· Difficulty 9.8374 Β· 6,665,658 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
805e403bd587da69199647be135ad46581c62278a7da73d08f406ca03c521c39
View on Chainz β†—

Height

#142,505

Difficulty

9.837373

Transactions

1

Size

200 B

Version

2

Bits

09d65e10

Nonce

5,724

Timestamp

8/31/2013, 12:18:56 AM

Confirmations

6,665,658

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

79d4b1f226b7c04a926ff3c5bc6e0918161c5e26e1fb08d3ee45633e2067d3fa
Transactions (1)
Coinbase79d4b1f226b7c0…45633e2067d3fa
1 in β†’ 1 out10.3200 XPM109 B
AL2EWWZm…CwsD5iKb
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.

2.325 Γ— 10⁹⁢(97-digit number)
23257384180076003230…53012709105191759679
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
2.325 Γ— 10⁹⁢(97-digit number)
23257384180076003230…53012709105191759679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.325 Γ— 10⁹⁢(97-digit number)
23257384180076003230…53012709105191759681
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
4.651 Γ— 10⁹⁢(97-digit number)
46514768360152006461…06025418210383519359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.651 Γ— 10⁹⁢(97-digit number)
46514768360152006461…06025418210383519361
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
9.302 Γ— 10⁹⁢(97-digit number)
93029536720304012923…12050836420767038719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.302 Γ— 10⁹⁢(97-digit number)
93029536720304012923…12050836420767038721
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
1.860 Γ— 10⁹⁷(98-digit number)
18605907344060802584…24101672841534077439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.860 Γ— 10⁹⁷(98-digit number)
18605907344060802584…24101672841534077441
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
3.721 Γ— 10⁹⁷(98-digit number)
37211814688121605169…48203345683068154879
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:57,709,350 XPMΒ·at block #6,808,162 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