XPM Prime Explorer symbol
XPMPrime Explorer

Block #132,685

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 2:08:31 AM Β· Difficulty 9.7896 Β· 6,671,328 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f238d804c9fdf700977baffa833f10a93d030a9244c49890faef70c1e1cef4cc
View on Chainz β†—

Height

#132,685

Difficulty

9.789588

Transactions

1

Size

200 B

Version

2

Bits

09ca226a

Nonce

242,541

Timestamp

8/25/2013, 2:08:31 AM

Confirmations

6,671,328

Mined by

⛏️ P2SHAHmvhRqWL5g4Fhy2RMfdSpypuGqgG5FwBR

Merkle Root

c06595a8abc7e0615df13ff723e501f310711a8ea43ec57d2b364562180681af
Transactions (1)
Coinbasec06595a8abc7e0…364562180681af
1 in β†’ 1 out10.4200 XPM109 B
AHmvhRqW…qgG5FwBR
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.

3.564 Γ— 10⁹⁢(97-digit number)
35645901809616610667…56379795637978295499
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
3.564 Γ— 10⁹⁢(97-digit number)
35645901809616610667…56379795637978295499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.564 Γ— 10⁹⁢(97-digit number)
35645901809616610667…56379795637978295501
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
7.129 Γ— 10⁹⁢(97-digit number)
71291803619233221334…12759591275956590999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.129 Γ— 10⁹⁢(97-digit number)
71291803619233221334…12759591275956591001
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
1.425 Γ— 10⁹⁷(98-digit number)
14258360723846644266…25519182551913181999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.425 Γ— 10⁹⁷(98-digit number)
14258360723846644266…25519182551913182001
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
2.851 Γ— 10⁹⁷(98-digit number)
28516721447693288533…51038365103826363999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.851 Γ— 10⁹⁷(98-digit number)
28516721447693288533…51038365103826364001
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
5.703 Γ— 10⁹⁷(98-digit number)
57033442895386577067…02076730207652727999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.703 Γ— 10⁹⁷(98-digit number)
57033442895386577067…02076730207652728001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,676,152 XPMΒ·at block #6,804,012 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